Chapter 7Chapter 7Proportional ReasoningProportional Reasoning

Section 7.3Section 7.3

Solving Percent ProblemsSolving Percent Problems

IntroductionIntroduction

David had a test score of 85 on a David had a test score of 85 on a test worth 100 points.test worth 100 points.

What fraction would represent his What fraction would represent his score? score?

Decimal?Decimal?Percentage?Percentage?

PercentPercent

A A percentpercent is a ratio with a is a ratio with a denominator of 100. denominator of 100.

Percent literally means “per Percent literally means “per hundred”.hundred”.

Percentages are a common base of Percentages are a common base of comparison because they can comparison because they can compare sets of different sizes.compare sets of different sizes.

Common percentages:Common percentages:

1%1% 10% 10% 25% 25% 50% 50%

100%100% 33 1/3 % 33 1/3 % 66 2/3 %66 2/3 %

Converting Fractions, Converting Fractions, Decimals, and PercentsDecimals, and Percents

Percent to DecimalPercent to Decimal

Decimal to PercentDecimal to Percent

Percent to FractionPercent to Fraction

Fraction to PercentFraction to Percent

Finding the Percent of a Finding the Percent of a NumberNumber

Examples:Examples:1.) 50% of 281.) 50% of 28

2.) 25% of 40002.) 25% of 4000

3.) A $25 shirt is selling at a 10% discount. 3.) A $25 shirt is selling at a 10% discount. Find the amount of discount and sale price.Find the amount of discount and sale price.

4.) A car manufacturer claimed that less than 4.) A car manufacturer claimed that less than 0.1% 0.1%

of seat belts fail in frontal accidents. If there of seat belts fail in frontal accidents. If there were 100,000 frontal accidents, what would be were 100,000 frontal accidents, what would be the maximum number of seat belts that could the maximum number of seat belts that could

be be expected to fail?expected to fail?

5.) Estimate 2% of 5275.) Estimate 2% of 527

Finding a Number when a Finding a Number when a Percent of it is KnownPercent of it is Known

Examples:Examples:

1.) The discount on a dress 1.) The discount on a dress

advertised as “1/3 off” is $55. advertised as “1/3 off” is $55.

What was the original price?What was the original price?

2.) George gave a $15 tip that 2.) George gave a $15 tip that

amounted to 18% of his total amounted to 18% of his total

restaurant bill. How much was the restaurant bill. How much was the bill?bill?

Find the Percent that one Find the Percent that one Number is of AnotherNumber is of Another

Examples:Examples:

1.) In a survey of 1500 people who 1.) In a survey of 1500 people who owned the same make of car, 900 owned the same make of car, 900 indicated that they would buy the indicated that they would buy the same make of car again. What same make of car again. What percent of these people were percent of these people were satisfied with their car?satisfied with their car?

2.)Kathy and Tommy are buying a 2.)Kathy and Tommy are buying a house that is listed for $127,500 and house that is listed for $127,500 and are paying $25,500 down. Find the are paying $25,500 down. Find the percent of the downpayment.percent of the downpayment.

Finding the Percent of Finding the Percent of Increase or DecreaseIncrease or Decrease

Determine the Determine the amount amount of increase of increase or decrease or decrease

Divide this amount by the Divide this amount by the originaloriginal amountamount

Convert this fraction or decimal to Convert this fraction or decimal to a percenta percent

new – oldnew – old

oldold

ExamplesExamples

1.) Attendance for a major league 1.) Attendance for a major league baseball team averaged 29, 500 for baseball team averaged 29, 500 for games in 1994 and 22,000 in 1995. games in 1994 and 22,000 in 1995. What was the percent decrease in What was the percent decrease in attendance from 1994 to 1995 (to attendance from 1994 to 1995 (to the nearest tenth of a percent)?the nearest tenth of a percent)?

2.) The number of student at a 2.) The number of student at a university increased from 6000 university increased from 6000 student in 1960 to 18,000 in 1968. student in 1960 to 18,000 in 1968. What was the percent increase in What was the percent increase in enrollment during this period?enrollment during this period?