Math 7 ( Period 4)

Solving  Percent Problems 7.5

There are 2 methods: Equations and Proportions

For both methods, there are THREE parts of any percent problem:

1) the BASE à the number you are taking a percent of

2) the PERCENT rateà the percent

3) the PERCENTAGE AMOUNT à (base)(%)

EQUATION METHOD:

Just translate and solve for the missing number.

Remember:

isà =

of à multiply

EXAMPLES:

Finding the PERCENTAGE AMOUNT

Find 60% of 15

First realize that “Find” means “What is”

and change the percent to a decimal or a fraction

so

What is 60% of 15

n = (.60)(15)

n = 9

Using fractions we found

first that 60/100 simplifies to 3/5

so

n =(3/5)(15)

That simplifies to

n = 9

Finding the BASE:

35% of what number  is 52.5

.35n = 52.5

simple one step equation

.35n/.35 = 52.5/.35

n = 150

Again, what if we used fractions

35% = 35/100 = 7/20

so

(7/20)n = 53.5

n = 150

Finding the PERCENT rate

What percent of 25 is 13?

25p = 13

p = 13/25

Now you need to make this a percent and that can be accomplished by dividing

but you can also use equivalent fractions   that is,

13/25 = 52/100 so that is 52%

PROPORTION METHOD

%/100 = is/of

Set this up each time and then substitute in what you know

Firstà look for the 5 rate and put that in ( if you are given it)

Second à find  either the “of” or the “is”

Lastà  Whatever is missing is what you are finding…

We did the three examples above as proportions

EXAMPLES:

Find 60% of 15

60/100 = x/15

Simplify and you get

3/5 = x/15

you can simplify even more and get

3/1 =x/3

so x = 3(3) = 9

35% of what number  is 52.5

35/100 = 52.5/x

Simplifying again we get

7/20 = 52.5/x

Using cross products

7x = 20(52.5)

7x = 1050

so x = 150

What percent of 25 is 13?

This is the only one where we do not have the %

n%/100 = 13/25

Can we simplify first?

Yes

n%/4 = 13/1

so n = 4(13)

n = 52

Remember to add the percent sign

52%