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In this professional development, basic math skills used to solve problems in animal systems will be explored. In particular, you will be studying these skills as they apply to poultry production, including, but not limited to, calculation of purchasing and marketing, housing requirements, and conversion of units. The mathematical concepts that you will focus on are addition, subtraction, multiplication, division, percentages, data analysis (reading tables) and area of two-dimensional objects.  

1. Determine the information missing to calculate percentage of live birds produced.

Egg-strain pullets are grown by the egg pullet operations to an age of 16 to 17 weeks before they go to the egg laying operations.

Producers brood and grow the pullets and are paid on the percentage of birds that reach production age.

To work problems involving percentages, you must understand multiplication and division of whole numbers, rational numbers, and integers. The conceptual understanding of percentages is begun in sixth grade. By the time students reach high school, they should master the concept. Percents are used in various ways in our society. Three of the most common uses for students is finding the percentage points on a test, annual interest rate on a savings account, or possibly the chance of rain.

"The word Percent comes from the Latin phrase per centum, which means per hundred" (Billstein, 2010, pg. 489). Thus, percents are nothing more than fractions. 45% is equivalent to (read 45 per 100 or forty-five hundredths). Thus, the definition of percent is n% = . Use the DragNDrop Activity below to practice matching the fraction to the percent.

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Answers

Like in multiplication of whole numbers, 3 cartons of 3 dozen eggs means to multiply 3 x (3x12) = 108 eggs. In percentages, 3% of 3 dozen eggs means to find 3/100 of 3 dozen eggs or x (3 x 12) = .03 x (3x12) = .03 x 36 = 1.08 (read one and eight one-hundredths). For more practice finding the percentage of numbers try your hand at the sorting activity below.

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Now use what you know about percentage to solve the following problem. If a producer is brooding 10,000 day-old-chicks and at 16 weeks he has 9,785 pullets to deliver to the egg laying operation, what would the production percentage be for this particular flock?

 To find the production percentage, you first have to divide 9,785 pullets by the original 10,000 day-old-chicks that you began with on day one. That gives you a decimal. To turn it into a percentage, you multiply the decimal by 100. For example 9,785 ÷ 10,000 X 100 = 97.85%

2. Determine the information needed to calculate the amount of feed needed to produce one dozen eggs.

Once the pullets reach 16 to 17 weeks of age they are moved to an egg laying operation. The egg laying operation is responsible for management of the birds during egg production phase. Most (ninety percent) of eggs produced commercially use caged hens in large environmentally controlled buildings. The typical commercial egg laying operation should produce one dozen eggs for every 3 to 3.5 pounds of feed consumed by the birds. 

To solve problems related to egg production and the amount of feed needed, you need to understand the basic operations of addition, subtraction, multiplication, and division with the sets of whole, rational, and integer numbers. As a mathematician, one should not be dependent on a calculator to do the calculations for you. You may find yourself in the middle of a field needing to do calculations and there is no calculator or paper and pencil to be found. As teachers, we need to be able to "play" with the numbers in ways that allow us to calculate large numbers mentally. Some of the algorithms used in developing mental math strategies are: Left-to-right, compensation, equal-additions, making tens, and the use of estimation when an exact answer is not needed.

As you work some basic math problems using various operations, you need to be aware of the order of operations. The following is the order in which problems should be worked: parenthesis, exponents, multiplication, division, addition, and subtraction. Even though multiplication is stated before division and addition before subtraction, the multiplication and division steps are worked in the order they occur, and then the addition and subtraction steps are performed in the order they occur. When solving problems with several operations and no parenthesis are used, the steps of multiplication and division are done before the addition and subtraction steps. Complete the following flash card activities by solving the problems presented and then click on the show button to check your answer.

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Next, try applying this basic math information to the following agricultural problem: If a commercial egg laying operations feeds 20,000 pounds of feed and produces 80,000 eggs, what is the amount of feed needed to produce one dozen eggs?

In this case, you are looking for the pounds of feed needed to produce one dozen eggs. First, you must determine how many dozen eggs are produced. This is determined by dividing the number of eggs produced by the number of eggs in one dozen (12).

80,000 eggs produced ÷12 eggs/dozen = 6666 dozen eggs produced.

To determine the amount of feed needed to produce one dozen eggs, you next take the amount of feed and divide it by the number of dozen eggs produced.

20,000 pounds of feed ÷ 6666 dozen eggs produced = 3.0003 pounds of feed needed to produce one dozen eggs

3. Determine the information needed to calculate the number of eggs produced per hen during the 52 to 80 week laying period.

To be able to solve a problem like this, you must know two of the following facts: how many laying hens, how many eggs produced, or how many eggs per hen. What information you are given will determine what operation you will use.

Look at solving the following problem. Commercial laying operations strive to produce 250 to 350 eggs per hen during the 52 to 80 week laying period. This is a typical length of time that a laying hen will be productive. If a commercial laying operation with 150,000 laying hens produces 45,000,000 eggs during a 70-week laying period, what is the number of eggs produced per hen during the laying period?

This particular problem only requires the use of division to find the answer (number of eggs per hen during a 70-week laying period). Thus, you divide the number of eggs during a 70-week laying period by the number of laying hens.

45,000,000 eggs ÷ 150,000 laying hens = 300 eggs per hen during the laying period.

If the problem is restated so that you are now looking for the number of laying hens, the problem only requires the use of division. For example: If a commercial laying operation produces 45,000,000 eggs during a 70-week laying period and 300 eggs per hen were laid, how many laying hens were used to produce that many eggs? You would need to divide the 45,000,000 eggs by 300 eggs per hen.

 45,000,000 eggs ÷ 300 eggs per hen = 150,000 laying hens.

Restating the problem a third way: If a commercial laying operation produces 300 eggs per hen in a 70-week laying period and 150,000 laying hens were used, how many eggs are produced during that laying period? Now you are looking for the total number of eggs produced over the 70-week laying period and you will have to use the operation of multiplication to solve the problem.

 300 eggs per hen x 150,000 laying hens = 45,000,000 eggs.

 4. Determine the information needed to calculate feed conversion of broiler chickens.

The first step in solving a problem is understanding the problem. Some strategies to use in understanding the problem are the following:

1) restate the problems in your own words;

2) identify what information you are given in the problem;

3) identify what it is you are trying to find or what is unknown;

4) identify information that is not needed.

Looking at the following information and problem, identify what you understand about the problem. On average, broilers are fed for 6 to 7 weeks and should reach 3.5 to 4.5 pounds. Two or less pounds of feed should be required to produce each pound of gain for a broiler chicken. Each broiler should dress into a 2 to 3 pound carcass for marketing.

Problem: If a commercial grow-out broiler operation produces 25,000 broiler chickens with a total weight of 100,000 pounds and consume 220,000 pounds of feed what is the feed conversion of the broiler chickens.

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Now that you've identified the information needed, it is time to solve the problem. The operation of division is needed to solve this problem. You will need to divide the total pounds of feed consumed by the total weight of broilers.

220,000 pounds of feed consumed ÷ 100,000 pounds of total weight of broilers = 2.2 pounds of feed per pound of gain.

5. Determine the information needed to calculate the square footage of space provided per bird in a commercial broiler grow-out operation.

Commercial grow-out operations for broiler chickens generally will grow birds in a large confinement house with about 0.8 square feet of floor space provided per bird. Contract production systems are used for 99 percent of broiler production. In solving these types of problems it is necessary to understand how to find the area or square footage of the floor space. Area of two-dimensional surfaces is a topic mastered by the time students finish junior high school. If the concept of area is developed correctly, students should not have to memorize numerous formulas, but can derive them from the formula of a rectangle (base x height). In this case, any side can be considered the base with the height being the distance between the two bases. For instance, the area of a triangle is ½ base x height. This can be shown easily with the following example of a rectangle that is 2" x 4". The ½ does not necessarily go with the length of the base, but is a constant showing what we are doing to the area of the rectangular region. Thus, the rectangle below can be divided into two equal parts to form two triangles. One of the triangles is ½ the area of the original rectangular region (b x h).

Table 5. Formulas for Areas of Regular Two-dimensional Figures.

Figure 2. Explanation of the Area of a Regular Octagon [add pop up defining Regular Polygon – A polygon that is both equilangular and equilateral (all angles are of equal measurement and sides are of equal measurement)

Similar to Figure 2, the area for irregular two-dimensional figures can be found by cutting the irregular figures into numerous regular figures and adding the areas of these regular figures together. This basis for this concept is taught as early as second and third grades.

Figure 3. The square footage of an L-shaped hen house.

The house in the following problem, as with most houses containing just hens, is rectangular in shape so that one does not have to do multi-steps to find the square footage of the hen house. Realistically, hen houses on large production farms may have several parts to them (control rooms, egg production, waste management, etc.), and one may be required to find the area of each section.

Problem: A farmer has 20,000 broilers and 2 houses, each has the dimensions of 40'X200'. What is the amount of space in square feet provided for each bird?

To work this problem, you have to find the square footage of each house.

40 ft X 200 ft = 8,000 square feet in each house

Next, multiply the square footage of one of the houses by 2 to get the square footage of both houses.

8,000 ft² X 2 = 16,000 ft² total space in the two houses

Next, to find the square footage per bird, divide the total square footage by the number of birds (per in this instance, means divide).

16,000 ft² ÷ 20,000 birds = 0.8 square feet per bird

6. Determine the information needed to calculate average daily gain in turkey production.

Facts: After hatching, young turkeys are taken to a grow-out facility. Male and female turkeys are grown in separate facilities. Most are raised in buildings with a smaller number raised in open range facilities. Turkey grow-out operations will generally have a capacity of 16,000 to 18,000 birds.

The feed conversion for turkeys should be approximately 2.5 pounds of feed per pound of gain. Twenty-pound hens will be produced and marketed at 16 weeks of age while tomes are marketed at 21 weeks of age and weigh 40 or more pounds.

Problem: If a farmer has 9,000 turkey hens that have a total weight of 189,000 and are marketed at 114 days of age, what is the average daily gain for these birds?

To solve this particular problem, you begin by dividing the total weight by the number of birds. This gives you the average weight per bird over the 114 days.

189,000 total weight ÷ 9,000 birds = 21-pound average bird weight

To find the average daily weight gain for the birds over the 114 days, you must divide the average bird weight over 114 days by 114 days.

21-pound average bird weight ÷ 114 days = .184 pounds of average daily gain.

7. Determine the information needed to calculate the per capita consumption of poultry products.

Poultry is a major contributor to employment and meat products in the United States.  Per capita consumption of poultry exceeds both beef and pork.  In 2010 the per capita consumption of chicken was 83.6 pounds and turkey had a per capita consumption of 16.4 pounds.  In comparison beef had 59.7 pounds, pork 48 pounds, fish 15 pounds, lamb 0.9 pounds and veal 0.4 pounds of per capita consumption.  Of the total United States per capita meat consumption 44.6 percent is poultry (both chicken and turkey).

Before we work this problem, let's practice finding percents:

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Problem: Calculate the percent per capita meat consumption in the United States that is made up of turkey meat consumption.

To solve this problem you must first know what the total pounds per capita consumption for each type of meat. You were given that information earlier.

     59.7 (beef) + 83.6 (chicken) + 15 (fish) + 0.9 (lamb) + 48 (pork) + 16.4 (turkey) + 0.4 (veal) = 224 total pounds per capita consumption

Next, you divide the total turkey consumption by the total meat consumption. 16.4 total turkey consumption ÷ 224 total meat consumption = .073

Next, you multiply the decimal by 100 (.073 X 100 = 7.32) to find what percent of the meat consumed was turkey.

8. Determine the information needed to convert waste water lagoon measurements into gallons.

Modern poultry facilities often produce large amounts of waste water which must be stored and treated. This waste can often be used as a nutrient source for crop production and water may be recycled for reuse in the flush systems of poultry buildings.  In most cases the water and poultry waste are stored in anaerobic lagoons. The anaerobic lagoons are used to degrade poultry waste.

A typical anaerobic lagoon for a 60,000 laying hen facility would be ten feet deep and have a surface area of 1.8 acres when filled to optimum water level. The lagoon would be located down slope from the poultry facility and would be a minimum of 300 feet from the nearest underground water well. 

Problem: Calculate the gallons of waste the above described lagoon would contain.

Sometimes a problem cannot be solved because not all the information is given. Also, there are times when information is given to understand the problem, but the numbers are not needed to solve the problem. Determine what information you are given that will help you solve the above problem, what information is given that does not directly effect the answer, and what information is still needed to solve the problem through the sorting activity below.

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In this case, you still needed to know that 1 acre foot is one acre of surface and one foot deep and contains 325,851 gallons. 

Thus, you would need to multiply the gallons per 1 acre foot times the number of acres - 325851 X 1.8 acres = 586,531.8 gallons per foot of depth

That answer gives you the number of gallons per 1 foot depth and you need the number of gallons when the lagoon is 10 feet deep.

586,531.8 X 10 feet of depth = 5,865,318 gallons of waste in the lagoon.

9. Determine the information needed to calculate incubation time for chicken eggs.

Facts: Stored eggs take longer to incubate.  For each day's storage beyond six days, the incubation time will be extended by one hour. Larger eggs take longer to incubate.  For each 0.1 ounce past 2.1 ounces of egg weight add 30 minutes to incubation time. Four-day-old eggs from 32-week-old chicken breeders normally require 21 days and 6 hours (510 hours) to incubate. 

Problem: How much time is required to incubate 11-day-old eggs from a 60 week old flock, with an average egg size of 2.6 ounces?

Sometimes, so much information is given that one needs to break the problem down into parts or smaller problems:

1. Decide what you are trying to find: Total incubation time for 11-day-old eggs with an average egg size of 2.6 ounces. Because they are older and weigh more than what is normally required, corrected incubation time must be found.

2. What is the fact: Stored eggs take longer to incubate. For each day's storage beyond six days, the incubation time will be extended by one hour. What I know from the problem: The eggs are 11 days old. That means the eggs were stored 5 more days beyond the six days. Thus, the eggs need to incubated 1 hour for each day extra in storage. Egg age Correction: 5 days extended storage X 1hour ÷ day = 5 hours

3. What is the fact: Larger eggs take longer to incubate. For each 0.1 ounce past 2.1 ounces of egg weight, 30 minutes needs to be added to the incubation time. What I know from the problem: The eggs weigh 2.6 ounces, 0.5 ounces above the 2.1 ounce egg weight. Thus, I need to add 30 minutes of 0.5 hours per 0.1 ounce. Since there are 0.5 ounces, I can multiply that amount times the 0.5 hours per 0.1 ounce (remember from earlier that per means divide). Egg size Correction: 0.5 ounce difference X 0.5 hour ÷ 0.1 ounce = 2.5 hours

4. Next you need to find the total correction time. To do this, you must add the egg age correction to the egg size correction. 2.5 hours + 5 hours = 7.5 hours. Remember that what you are trying to find is the total time it would take to incubate the eggs. All that you have found is the corrected time.

5. To find the total time, you will need to add the time normally required to incubate the egg and add it to the total corrected time. Total time to incubate the 11-day-old eggs with an average egg size of 2.6 ounces: 510 hours + 7.5 hours = 517.5 hours (21 days and 13.5 hours) 

10. Determine the information needed to determine the percentage of uniformity of a broiler flock.

A sample of body weights are taken from a flock of finished broiler chickens to determine an estimate of body weight uniformity.  Estimates are reported as the percentage of individual weights that fall within a specified range.

The range is generally reported as the average weight of flock samples plus or minus 15%.  For a flock of broilers with an average body weight of 2 pounds, the common uniformity measure is 2+ = 1.7 to 2.3 pounds.  The percentage of the sample weights that fall within 1.7 and 2.3 pounds is the percentage uniformity of the flock.

Problem: If a flock has an average sample weight of 2 pounds and we use a uniformity range of 15% and have 89 of 100 birds fall within this range, what is the percentage uniformity? 

In this case the uniformity percentage would simply be 89% since 89 of 100 birds would be 89%.

11. Calculate the amount of lighting needed for normal egg production in laying hens.

Facts: Light is required for a chicken to lay eggs as light stimulus is provided to the chicken when light enters the chicken's eye.  Only about 0.25fc of light is needed for a chicken to see how to eat, but 0.5 to 1 fc is needed to stimulate the pituitary to release luteinizing hormone (LH) and follicle stimulating hormone (FSH), which causes increased growth of the ova.  Chickens have color vision and see better when red, orange, yellow or blue lighting is used.  Control of lighting in the house is essential to good egg production as it influences egg size, egg numbers, and livability of chickens.

Never increase light duration during the growing phase of laying chickens.  A program of decreasing light duration is usually used. Lighting of 22 hours used at the beginning of the brooding process and is decreased down to 8 hours by the time birds are 8 - weeks old. A reduction in the amount of light by 1.75 hours per week is often used.

Never decrease light duration or light intensity during the laying phase.  Once birds reach 2.8 pounds of weight, start increasing the light duration until it reaches 16 hours of daily lighting.  The light intensity should be 1 to 3 fc.

A watt is the amount of electric energy consumed and the amount of light emitted by a light source.  One watt from an incandescent light bulb on average equals 12.56 lumens. A Compact Flourescent Lamp (CFL) averages about 62.5 lumens per watt. A Foot-candle (fc) equals one lumen per square foot.

About 30% of the light from a poultry house is absorbed by the walls, ceiling and equipment.  Only about 49 percent of the lighting system is available to the chickens in the building. If a 100-watt incandescent bulb produces 1256 lumens (100x12.56) only 615.4 lumens (1256 X 49%) are available to the chickens.  This should be sufficient lighting for 307.7 square feet of space (one fc equals one lumen per square foot, using 2 fc per square).

Problem: Using the above information about hours of lighting needed, what is the amount of lighting needed for 6-week old birds?

To find the amount of lighting, you must realize that the amount of lighting is decreased each week until they are 8-weeks old. Since 6-weeks is less than 8-weeks, you will be subtracting the reduction of lighting from the beginning lighting.

22 hours at beginning of brooding process - (6 weeks x 1.75 hours per week) = 22 hours - 10.50 hours = 11.50 hours

Problem: You must plan a lighting system for a 30 x 50 egg laying facility with light colored walls and ceiling. The ceiling height is 8 feet. Research shows that 2 fc is needed for egg production. General lighting guidelines for light while chickens are laying requires 1 lumen per square foot per foot-candles. If only 49% of the lighting system is available to the chickens in the building, what is the total number of lumens available to the chickens.

Floor area - 30' x 50' = 1,500 square feet.

1,500 square feet x 1 lumens per square foot per foot-candles = 1,5000 lumens for each foot-candle requirement.

3,000 lumens per foot-candle x 50 foot-candles = 150,000 lumens.

150,000 lumens x 49% = 73,500 lumens

Many times so much information is given that one needs to find a way to organize that information, a skill that is most helpful in any career. The use of tables is one way to organize related data in rows and columns so that the reader can quickly see the data being presented. Not only does one need to be able to organize the data in a table, but must also be able to read and analyze data presented by others. Sometimes the organization of a table will allow a person to quickly analyze the information for patterns that might be occurring. Other times, the use of tables allows one to organize data that can later be graphed. No matter how they are used, tables allow one to organize the data so that it makes sense to the reader. A table should always have a title and labels indicating what information is being presented. In an article in the Poultry Engineering, Economics, and Management Newsletter, the U. S. Poultry & Egg and Alabama Poultry & Egg Associations present information regarding research on the types of light bulbs to use in hen houses. On page 3, they have a good example of presenting a lot of information in a table. Use that table to answer the true/false statement in the following Self Check.

Problem: Using the table below, determine how the percentage of FAN KWH and Light KWH for Flock number 4 was found.

Electrical Usage & Economics Summary Table - Incandescent vs. Cold Cathode/Compact Florescent Light (CC/CFL) Combinations

For five flocks in a typical 40' x 500' solid wall, tunnel ventilated broiler house, North Alabama, 2008-2009.

To determine the percentage of KWH for the fan and light KWH usage, the following mathematical steps must be conducted:

The percent of KWH for fan = amount of Fan KWH divided by the Total KWH:

1. 1,371 ÷ 3,172 = .4322194199
2. Round this answer to the nearest hundredth, which is .43
3. To find the percentage: .43 x 100 = 43%
4.  

The percent of KWH for light is equal to the amount of light KWH divided by the Total KWH:

1. 523 ÷ 3,172 = .1648802018
2. Round this answer to the nearest hundredth, which is .16
3. To find the percentage: .16 x 100 = 16%

 It is very important to check the information given in tables and charts. There inadvertently may be some wrong information. In the table above, there are two mistakes. Use the Test Yourself below to determine what information is incorrect.

12. Calculate dressing percentage and carcass yield of animals commonly used for meat production

The dressing percentage is the percent of the live animal that ends up as carcass. Generally, the carcass weight is taken immediately after skinning and evisceration and is commonly known as the hot hanging weight. There are a number of factors that will affect the percentage including how much the animal has eaten before it is weighed, how much mud or fiber is on the animal. These factors negatively correlate to the dressing percentage, by reducing the dressing percentage. The amount of fat and muscling will positively affect dressing percentage, the heavier or fatter an animal, the higher the dressing percentage. The dressing percentage can be calculated as such: Dressing Percentage (DP)= (Carcass Weight / Live Weight) x 100. Different species tend to average different DP's. Beef cattle average 62%, steers 59%, hogs 74% and market lambs 54%. Farmers can expect a 1000 pound steer to result in a 620 pound hanging carcass or a 140 pound market hog to produce a 103 pound carcass (140 x .74).

The carcass-cutting yield is the percentage of the carcass that actually ends up as meat. The carcass cutting yield is calculated by: (Pounds of meat/ Carcass weight) x 100. Cutting yields can vary significantly depending upon cutting specifications; cuts that are bone-in or boneless, will produce very different cutting yields. If the animal is excessively fat, then the cutting yield will be lower because the fat is removed and discarded. A more muscular animal will have a higher cutting yield. Aging, leaving the carcass to hang for an extended period of time, will also impact cutting yields, as the carcass tends to shrink during the process. Cutting losses on a side of beef may range from 20 to 40 percent, and average around 28%.

Problem:  Determine the average Dressing Percentage for a whole chicken if you know that broilers are fed for 6 to 7 weeks and should reach 3.5 to 4.5 pounds and should dress into a 2 to 3 pound carcass for marketing.

• To find an average weight of a broiler based on range of weights, do the following calculations: 3.5 pounds + 4.5 pounds = 8 pounds; 8 pounds ÷ 2pounds = 4 pounds

• To find an average weight of a carcass based on range of weights, do the following calculations: 2 pounds + 3 pounds = 5 pounds; 5 pounds ÷ 2 pounds = 2.5 pounds

• To find the Dressing Percentage divide weight of broiler by weight of carcass and multiply by 100. 2.5 pounds ÷ 4 pounds = 0.625; 0.625 x 100 = 62.5%

13. Calculate Feed Conversion Ratio(FCR) for different types of animals.

Facts: Specifically FCR is the mass of the food eaten divided by the body mass gain, all over a specified period of time.  It is often expressed for the amount of time an animal is on a specific feeding system, but also may be measured for an age period of the animal.  The FCR for cattle and sheep in a feedlot may be 8 pounds of feed per pound of gain.  Swine will generally have a feed conversion of 3-4 pounds of feed per pound of gain.  Broilers will usually have a 2 to 1FCR.  Fish will often have a 1.2-1.8 to 1 FCR.

Problem: Find the FCR if a chicken has a mass gain of 0.8 grams and was fed 1.2 grams of grain.

FCR = 1.2 grams ÷ .8 grams = 1.5

14. Calculate the percentage of heterosis for various traits in differing species of livestock.

Facts: Heterosis, or hybrid vigor, is the name given the biological phenomenon that causes crossbreeds to out produce the average of their purebred parents.  For a large number of traits the performance of the cross is superior to the average performance of the parents. These traits includes size, growth rate, fertility, and yield of a hybrid organism.

Heterosis is measured by the amount the crossbred offspring exceeds the average of the two parent breeds for a particular trait.  The following formula can be used to calculate percent heterosis for any one trait:(Crossbred average – Straightbred average) ÷ StraightbredAverageX 100 = Percent Heterosis of hybrid vigor

Problem: If the average litter weaning weight for a group of crossbred pigs is 340 pounds and the average for the two parents' lines is 280 pounds, what is the heterosis?

340 pounds - 280 pounds = 60 pounds

(60 pounds ÷ 280 pounds) = .2142857143

.2142857143 x 100 = 21.42857243 or 21%

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