Solving Percent ProblemsSolving Percent Problems

Mrs. Maher

Rate and Ratio ReviewRate and Ratio Review

RatiosRatios(4 forms of a ratio)(4 forms of a ratio)

1) 5 flutes to 2 guitars

2) Of the students got an A.

3) 3 boys : 2 girls

4) 4 out of 5 students had their homework

RatesRates(simplify so that you get (simplify so that you get

“per” unit)“per” unit)1) 6 gallons for $6.75

$1.13 per gallon

2) Sold 120 rings in 8 h15 per hour

3) Drove 50 miles in 2 hours

25 miles per hour

4

3

Solving a ProportionSolving a Proportion

13

4

12)b

13

4

12)b

b = 1Solve using equivalent fractions

x4

x4

128

6)2

r

6 x 12 = 8r

72 = 8r

72 / 8 = r

9 = r

Solve using cross products

Finding Percent of a NumberFinding Percent of a Number

Solve using fractions Solve using decimalsFind 50% of 25 Find 35% of 70

2

112

2

25

1

25

2

1

0.35 x 70 = 24.5

Percent of a NumberPercent of a Number(using a proportion to solve)(using a proportion to solve)

• We can use proportions to solve all percent problems.

100

%

of

is

So when we don’t know the “of” or the “%” we can use a proportion to solve.

Percent of a Number:Percent of a Number:Solve for “is”Solve for “is”

• What is 16% of 50?What is 16% of 50?

• You could change the percent to a decimal or fraction and multiply.

• OR You could set up a proportion and use cross products or equivalent fractions to solve:

a

50

16

100

100

%

of

is

Percent of a Number:Percent of a Number:solve for “is”solve for “is”

1) What is 24% of 50?1) What is 24% of 50?

100

%

of

is

50100

24 x

2

2X = 12

Check: Use Cross products!!

Solve using equivalent fractions (or cross products)

Percent of a NumberPercent of a Number

• Finding the “of”Finding the “of”

• Do the same thing, but solve for “of”.

• 90 is 75% of what 90 is 75% of what number?number?

100

%

of

isx

90

100

75

Use Cross Products to solve, then check.

X = 120

Percent of a Number:Percent of a Number:Solving for the %Solving for the %

• What if you don’t know the percent?

• Well, you can use the same proportion, but solve for the percent.

• 17 is what percent 17 is what percent of 20?of 20?

100

%

of

is

Percent of a NumberPercent of a Number

• Find the percent.

1)1) 21 is what percent of 21 is what percent of 30?30?

2)2) On a 50 point quiz, On a 50 point quiz, you received 48 you received 48 points. What percent points. What percent did you receive?did you receive?

3) On a 40 point quiz, you 3) On a 40 point quiz, you received 38 points plus received 38 points plus 6 bonus points. What is 6 bonus points. What is the percent?the percent?