Math 6 High ( Period 3)

Solving Percent Problems 7.4

You can use a proportion to find what percent one number is of another number.
The statement:

“ a is p percent of b” is expressed by the proportion shown below where

a is the  part of the base      b is the base… and    p is the percent

a/b = p/100

Part of the base / base = percent/100

What percent of 40 is 15?

First think which is the base? 40

Which number is the part?  15

Now write the proportion

a/b = p/100

15/40 =  p/100

Use cross products to multiply… simplify first if you can…

15(100) = 40p

Divide both sides by 40

15(100)/40 = 40p/40

37.5 = p

Note: there are a number of ways to simplify first! You should still arrive at p = 37.5 which means 37.5%

Finding a Percent

Your team won 19 of its 25 softball games. What percent did it win?

Games won/games played = percent/100

It really is still      a/b = p/100

19/25 = p/100

19(100) = 25p

Divide both sides by 25

19(100)/25 = 25p/25

76= p

Again there are a variety of ways to simply BEFORE you multiply! You could even utilize the equivalent fraction method to determine the p percent.

Therefore your team won 76% of its games!

You can use the proportion to find a base or a part of the base.

Finding a part of the base

You buy a pair of pants on sale. The price is 80% of the regular price of $24.50, WOW! That’s a bargain! What is this incredible sales price?

Sale price / regular price = Percent/100

a/24.50 = 80/100

Multiply and divide carefully

100a = 24.50(80)

divide both sides by 100

100a/100 = (24.50)(80)/100

a = 19.6

The sale price is $19.60

Now, you could use the writing an equation method

80% of 24.50 = sale price  or

(.80) (24.50) = p

Multiply carefully

19.60 = p

$19.60 is the sale price.

Finding a Base

8 is 32% of what number?

Method 1: Write and solve a proportion

a/b = p/100

8/b = 32/100
Using cross products
(8)(100) = 32b
Divide both sides by 32

(8)(100)/32 = 32b/32

25 = b

Method 2: Write and solve an equation

8 is 32% of what number?
8 = .32(x)

8/.32 = .32x/.32
Divide carefully

25= b

8 is 32% of 25

Solving Percent Problems

a/b = p/100   means a is p percent of b

Out of 80 students taking Algebra, 95% passed the final exam. About 80% of those who passed the exam got a grade better than a C. How many students got an A or a B?

First find out how many passed the final exam

Using the proportion method for this:

a/80 = 95/100

100a = 80(95)

100a/100 = (80)(95)/100

a = 76

76 students passed the final exam

About 80% of 76 got a grade better than a C

Using the writing an equation method

(.80)(76)  =60.8

Since you can’t have a part of a student your answer would be about 61 students got an A or a B in Algebra