Math 074: Review for Chapter 6 Test – Sections 6.1, 6.2, and 6.3
In order to prepare for the Chapter 6 Test, you need to understand and be able to work
problems involving the following topics:
I.
Percent Models:
Can you draw a model of a percent?
Ex1: Draw a picture to illustrate 42%.
II.
Equivalent Forms:
A. Can you convert percents to fractions?
Ex2: Convert each of the following percents to fraction form in lowest
terms:
1) 23%
2) 42%
3) 145%
4) 0.3%
B. Can you convert percents to decimals?
Ex3: Convert each of the following percents to decimal form:
1) 23%
2) 410%
3) 0.5%
C. Can you convert fractions to percents?
Ex4: Convert each of the following fractions to percent form:
1)
1
3
2)
7
8
3)
3
5
D. Can you convert decimals to percents?
Ex5: Convert each of the following decimals to percent form:
1) 0.145
2) 0.8
3) 2.63
4) 0.009
III.
Key Vocabulary:
Can you identify the amount, base, and percent in a given situation?
Ex6: Identify the amount, base, and percent in each of the following:
1) 6 is 12% of 50.
2) Michigan charges 6% sales tax. The sales tax on a $24 purchase
is $1.44.
IV.
Solve Basic Percent Problems:
A. Can you solve problems in which you are asked to find the amount when
given the base and the percent?
Ex7: Solve the following:
1) What is 14% of 36?
2) What is 105% of 67?
3) At one time, Polish-Americans constituted 97% of the
population of Hamtramck, MI. How many Polish-Americans
lived in the city if its population was 24,000 persons?
B. Can you solve problems in which you are asked to find the percent when
given the base and the amount?
Ex8: Solve the following:
1) What percent of 50 is 8?
2) 15 is what percent of 60?
3) A snack food contains 80 calories, and 30 calories are from fat.
What percent of the calories are from fat?
C. Can you solve problems in which you are asked to find the base when
given the percent and the amount?
Ex9: Solve the following:
1) 14 is 87.5% of what number?
2) 18% of some number is 36. What is the number?
3) 30% of students in a class are male. How many students are in
the class if there are 12 men in the class?
V.
Solve Percent Increase and Decrease Problems:
A. Can you solve problems in which some quantity increases and you want to
determine what percent of the original quantity this increase is?
Ex10: Solve the following:
1) During a power outage, the price of gasoline jumped from $1.60
per gallon to $1.75 per gallon. What was the percent increase?
2) The population of a town was 14,600 persons in 1990 and
16,000 persons in 2000. What was the percent increase in the
town’s population from 1990 to 2000? Round your answer to 2
decimal places.
B. Can you solve problems in which some quantity decreases and you want to
determine what percent of the original quantity this decrease is?
Ex11: Solve the following:
1) A restaurant charges $1.20 for a cup of coffee. However, senior
citizens are only charged $0.75. What is the percent reduction
for senior citizens?
2) With a grocery store card, a person can purchase a container of
orange juice for $0.67. Without the card, the orange juice costs
$1.19. What is the percent decrease in the price with the card?
Round your answer to one decimal place.
VI.
Solve Tax, Commission, Mark-up, and Discount Problems:
A. Can you solve word problems involving taxes?
Ex12: Solve the following:
1) In one location, state and local sales taxes combine for a total of
8.5%. What is the amount of sales tax on an item that costs
$129?
2) A person purchases items marked $2.95, $12.99, $6.97, and
$4.19. What is the total cost of these purchases including
Michigan’s 6% sales tax?
B. Can you solve word problems involving a salesperson’s commission?
Ex13: Solve the following:
1) A certain car dealership pays its sales people $500 per week
plus 3% commission. How much does a sales person earn for a
week in which she sells $36,000 worth of cars?
2) A friend asks your advice regarding a job situation. He can
accept a sales job that pays $650 per week, or a sales job that
pays $400 per week plus a 9% commission. He learns that for
the second job, other people are usually earning commissions
on $2,500 worth of sales per week. Which job would you
recommend to your friend?
C. Can you solve word problems involving the mark-up of an item’s price?
Ex14: Solve the following:
1) You need to set the price for the lemonade at your lemonade
stand. If it costs you $0.05 per cup to make the lemonade and
you want to earn a 300% profit on a cup, at what price will you
sell a cup of lemonade?
2) A stock clerk is told to place a price tag on an item with a
mark-up of 17%. What is the price on the tag if the item costs
the store $6?
D. Can you solve word problems involving discounts, like sales?
Ex15: Solve the following:
1) A local nursery is having a 30% off sale. What is the sale price
of an evergreen tree that was originally priced at $299.99?
2) An item regularly priced at $7.99 is on sale for $5.99. What is
the percent discount? Round your answer to the nearest whole
percent.
3) A pair of shoes that is on sale for 40% off is marked with a sale
price of $75. What was the original price of the shoes?
Answers:
Ex1:
Ex2: 1)
23
100
Ex3: 1) 0.23
2)
42 21
=
100 50
2) 4.1
1
Ex4: 1) 33.3% or 33 %
3
Ex5: 1) 14.5%
3)
145 29
=
100 20
4)
3
1000
3) 0.005
1
2) 87.5% or 87 %
2
2) 80%
3) 263%
3) 60%
4) 0.9%
Ex6: 1) amount = 6, base = 50, percent = 12%
2) amount = $1.44, base = $24,
percent = 6%
Ex7: 1) 5.04
2) 70.35
3) 23,280
Ex8: 1) 16%
2) 25%
3) 37.5%
Ex9: 1) 16
2) 200
3) 40
Ex10: 1) 9.375%
2) about 9.59%
Ex11: 1) 37.5%
2) about 43.7%
Ex12: 1) $10.97
2) $28.73
Ex13: 1) $1,580
2) The first job ($650 per week) because 9% of the usual
$2500 sales plus $400 is only $625.
Ex14: 1) $0.20
2) $7.02
Ex15: 1) $209.99
2) 25%
3) $125