6.8.1: Review Exercises
- Page ID
- 118946
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Review Exercises
Understand Percent
In the following exercises, write each percent as a ratio.
admission rate for the university
rate of college students with student loans
In the following exercises, write as a ratio and then as a percent.
out of architects are women.
out of every nurses are men.
In the following exercises, convert each percent to a fraction.
In the following exercises, convert each percent to a decimal.
4.9%
In the following exercises, convert each percent to ⓐ a simplified fraction and ⓑ a decimal.
In of the United States population was age or over. (Source: www.census.gov)
In of the United States population was under years old. (Source: www.census.gov)
When a die is tossed, the probability it will land with an even number of dots on the top side is
A couple plans to have three children. The probability they will all be girls is
In the following exercises, convert each decimal to a percent.
In the following exercises, convert each fraction to a percent.
According to the Centers for Disease Control, of adults do not take a vitamin or supplement.
According to the Centers for Disease Control, among adults who do take a vitamin or supplement, take a multivitamin.
In the following exercises, translate and solve.
What number is of
of is what number?
is of what number?
is of what number?
of what number is
of what number is
What percent of is
What percent of is
Solve General Applications of Percents
In the following exercises, solve.
When Aurelio and his family ate dinner at a restaurant, the bill was Aurelio wants to leave of the total bill as a tip. How much should the tip be?
One granola bar has grams of fiber, which is of the recommended daily amount. What is the total recommended daily amount of fiber?
The nutrition label on a package of granola bars says that each granola bar has calories, and calories are from fat. What percent of the total calories is from fat?
Elsa gets paid per month. Her car payment is What percent of her monthly pay goes to her car payment?
In the following exercises, solve.
Jorge got a raise in his hourly pay, from to Find the percent increase.
Last year Bernard bought a new car for This year the car is worth Find the percent decrease.
Solve Sales Tax, Commission, and Discount Applications
In the following exercises, find ⓐ the sales tax ⓑ the total cost.
The cost of a lawn mower was The sales tax rate is of the purchase price.
The cost of a water heater is The sales tax rate is of the purchase price.
In the following exercises, find the sales tax rate.
Andy bought a piano for The sales tax on the purchase was
Nahomi bought a purse for The sales tax on the purchase was
In the following exercises, find the commission.
Ginny is a realtor. She receives commission when she sells a house. How much commission will she receive for selling a house for
Jackson receives commission when he sells a dinette set. How much commission will he receive for selling a dinette set for
In the following exercises, find the rate of commission.
Ruben received commission when he sold a painting at the art gallery where he works. What was the rate of commission?
Tori received for selling a membership at her gym. What was her rate of commission?
In the following exercises, find the sale price.
Aya bought a pair of shoes that was on sale for off. The original price of the shoes was
Takwanna saw a cookware set she liked on sale for off. The original price of the cookware was
In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.
Nga bought a microwave for her office. The microwave was discounted from an original price of
Jarrett bought a tie that was discounted from an original price of
In the following exercises, find ⓐ the amount of discount ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.)
Hilda bought a bedspread on sale for The original price of the bedspread was
Tyler bought a phone on sale for The original price of the phone was
In the following exercises, find
- ⓐ the amount of the mark-up
- ⓑ the list price
Manny paid a pound for apples. He added mark-up before selling them at his produce stand. What price did he charge for the apples?
It cost Noelle for the materials she used to make a purse. She added a mark-up before selling it at her friend’s store. What price did she ask for the purse?
Solve Simple Interest Applications
In the following exercises, solve the simple interest problem.
Find the simple interest earned after years on invested at an interest rate of
Find the simple interest earned after years on invested at an interest rate of
Find the principal invested if interest was earned in years at an interest rate of
Find the interest rate if interest was earned from a principal of invested for years.
Kazuo deposited in a bank account with interest rate How much interest was earned in years?
Brent invested in a friend’s business. In years the friend paid him the plus interest. What was the rate of interest?
Fresia lent her son for college expenses. Three years later he repaid her the plus interest. What was the rate of interest?
In years, a bond that paid earned interest. What was the principal of the bond?
Solve Proportions and their Applications
In the following exercises, write each sentence as a proportion.
is to as is to
miles to gallons is the same as miles to gallons.
teacher to students is the same as teachers to students.
for ounces is the same as for ounces.
In the following exercises, determine whether each equation is a proportion.
In the following exercises, solve each proportion.
In the following exercises, solve the proportion problem.
The children’s dosage of acetaminophen is milliliters (ml) for every pounds of a child’s weight. How many milliliters of acetaminophen will be prescribed for a pound child?
After a workout, Dennis takes his pulse for sec and counts beats. How many beats per minute is this?
An ounce serving of ice cream has calories. If Lavonne eats ounces of ice cream, how many calories does she get?
Alma is going to Europe and wants to exchange into Euros. If each dollar is Euros, how many Euros will Alma get?
Zack wants to drive from Omaha to Denver, a distance of miles. If his car gets miles to the gallon, how many gallons of gas will Zack need to get to Denver?
Teresa is planning a party for people. Each gallon of punch will serve people. How many gallons of punch will she need?
In the following exercises, translate to a proportion.
What number is of
is of what number?
What percent of is
What percent of is
In the following exercises, translate and solve using proportions.
What number is of
of what number is
is of what number?
What percent of is