Percent problems may be solved using several different methods. One method uses multiplication by a constant factor. Work through the examples below to examine the constant factor method as well as a few other methods.

Try the following two examples.

Example 1:

Freddie is downloading a program that is 1.5 megabytes. According to the progress bar, it has finished 30% of the download. How many megabytes have been downloaded so far?

On a separate piece of paper, draw a percent bar that represents how you would use a percent bar to find the amount of data that has been downloaded so far.

What does the problem give you?

Interactive popup. Assistance may be required. Check Your Answer Total size is 1.5 megabytes.
30% has been downloaded.

What does the problem ask for?

Interactive popup. Assistance may be required. Check Your Answer The problem asks for the number of megabytes that have been downloaded so far.

Interactive popup. Assistance may be required. Click here to see an example of a percent bar.
10% of 1.5 = 0.15
3(0.15) = 0.45
30% of 1.5 = 0.45
0.45 megabytes have been downloaded

Try solving the problem using a proportion.
Copy the following table into your notes and fill in the missing information:

Click here to see the completed table.

	Percent	megabytes
Part	30	m
Whole	100	1.5

Use the chart to set up a proportion relating the percent to the number of megabytes:

Interactive popup. Assistance may be required. Check Your Answer 30 over 100 30 100 = m over 1.5 m 1.5

Use this proportion to find m, the number of megabytes downloaded so far.

Interactive popup. Assistance may be required. Check Your Answer 100m = (30)(1.5)
100m = 45
m = 0.45
0.45 megabytes have been downloaded.

Finally, let's try the same problem by using an equation.
What is your plan to solve the equation?

Interactive popup. Assistance may be required. Check Your Answer Multiply the percent that has been downloaded by the total size of the file.

Write your plan as an equation.

Interactive popup. Assistance may be required. Check Your Answer m = 0.3(1.5)

How many megabytes have been downloaded?

Interactive popup. Assistance may be required. Check Your Answer m = 0.3(1.5)
m = 0.45
0.45 megabytes have been downloaded.

Example 2:
You want to buy a television in an electronics store that offers a payment plan so that you can make payments every month instead of paying all at once. To qualify for the payment plan, the store requires you to make a 20% payment today.

If the television originally cost $1100, how much do you need to pay today?

Interactive popup. Assistance may be required. Click here to see the percent bar.

10% of 1100 = 110
2(110) = 220
20% of 110 = 220
You need to pay $220 today.

Use each of the methods described below to solve this problem then click to check your answer.

Create a data table and use it to write a proportion relating the percent to the price you need to pay today.

Interactive popup. Assistance may be required. Check Your Answer

	Percent	megabytes
Part	20	p
Whole	100	1100

20 over 100 20 100 = p over 1100 p 1100
100p = (20)(1100)
100p = 22000
p = 220
You need to pay $220 today.

Write and solve an equation that you could use to solve for the p, the payment you need today if the television has an original cost of c dollars.

Interactive popup. Assistance may be required. Check Your Answer Equation
p = 0.2c
p = 0.2 (1100)
p = 220
You need to pay $220 today.

When solving equations in the form of y = kx, multiplying by a percent will help you find a part of the larger whole.