1.5.1: Exercises

Last updated
Save as PDF

Page ID: 74287

Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia
Rio Hondo College

$ \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}}} $

$\newcommand{\avec}{\mathbf a}$ $\newcommand{\bvec}{\mathbf b}$ $\newcommand{\cvec}{\mathbf c}$ $\newcommand{\dvec}{\mathbf d}$ $\newcommand{\dtil}{\widetilde{\mathbf d}}$ $\newcommand{\evec}{\mathbf e}$ $\newcommand{\fvec}{\mathbf f}$ $\newcommand{\nvec}{\mathbf n}$ $\newcommand{\pvec}{\mathbf p}$ $\newcommand{\qvec}{\mathbf q}$ $\newcommand{\svec}{\mathbf s}$ $\newcommand{\tvec}{\mathbf t}$ $\newcommand{\uvec}{\mathbf u}$ $\newcommand{\vvec}{\mathbf v}$ $\newcommand{\wvec}{\mathbf w}$ $\newcommand{\xvec}{\mathbf x}$ $\newcommand{\yvec}{\mathbf y}$ $\newcommand{\zvec}{\mathbf z}$ $\newcommand{\rvec}{\mathbf r}$ $\newcommand{\mvec}{\mathbf m}$ $\newcommand{\zerovec}{\mathbf 0}$ $\newcommand{\onevec}{\mathbf 1}$ $\newcommand{\real}{\mathbb R}$ $\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$ $\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$ $\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$ $\newcommand{\laspan}[1]{\text{Span}\{#1\}}$ $\newcommand{\bcal}{\cal B}$ $\newcommand{\ccal}{\cal C}$ $\newcommand{\scal}{\cal S}$ $\newcommand{\wcal}{\cal W}$ $\newcommand{\ecal}{\cal E}$ $\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$ $\newcommand{\gray}[1]{\color{gray}{#1}}$ $\newcommand{\lgray}[1]{\color{lightgray}{#1}}$ $\newcommand{\rank}{\operatorname{rank}}$ $\newcommand{\row}{\text{Row}}$ $\newcommand{\col}{\text{Col}}$ $\renewcommand{\row}{\text{Row}}$ $\newcommand{\nul}{\text{Nul}}$ $\newcommand{\var}{\text{Var}}$ $\newcommand{\corr}{\text{corr}}$ $\newcommand{\len}[1]{\left|#1\right|}$ $\newcommand{\bbar}{\overline{\bvec}}$ $\newcommand{\bhat}{\widehat{\bvec}}$ $\newcommand{\bperp}{\bvec^\perp}$ $\newcommand{\xhat}{\widehat{\xvec}}$ $\newcommand{\vhat}{\widehat{\vvec}}$ $\newcommand{\uhat}{\widehat{\uvec}}$ $\newcommand{\what}{\widehat{\wvec}}$ $\newcommand{\Sighat}{\widehat{\Sigma}}$ $\newcommand{\lt}{<}$ $\newcommand{\gt}{>}$ $\newcommand{\amp}{&}$ $\definecolor{fillinmathshade}{gray}{0.9}$

Section 1.5.1

Write each percent as a fraction.
1. 87%
2. 40%
3. 110%
Write as a percent.
1. 5858
2. 4545
Write each percent as a decimal.
1. 27%
2. 8.328%
3. 125%
4. 0.5%
Change each decimal to a percent.
1. 0.34
2. 2.5
3. 0.0045
50 is 40% of what number?
A shirt that usually sells for $25 is on sale for $21. What is the percent decrease in the price of the shirt?
A car salesman has a commission rate of 12% on the cars sold. If the commission on one sale was $1836, what was the purchase price of the car?
You purchase an item originally priced at $240 that is discounted 30%. What is the sale price of the item?
You pay sales tax of 9.5% on your purchase. What is the total cost for your purchase with the discount and the sales tax?
The sales clerk accidentally added the sales tax based on the original price of your purchase before giving you a 30% discount. Would this error cause the item to cost you more or less or the same as what you figured in part b)?
A store advertises a 40% off clearance sale. When you arrived at the store, you received a coupon for an additional 10% off. The coupon is applied after the 40% discount.
1. What is the total discount if the item is normally priced at $30?
2. What is the total discount percent?
3. Why do you think the store uses two discount percents instead of one? Explain.
Consider the following.
1. A parenting blog states that 12-year-old girls typically weigh 200% of what 6-year-old girls weigh? Does that mean a girl’s weight doubles between ages 6 and 12?
2. Could it be true that an 8-year-old girl weighs 30% more than a 6-year- old girl?
Out of 230 racers who started the marathon, 212 completed the race, 14 gave up, and 4 were disqualified. What percentage did not complete the marathon?
Patrick left an $8 tip on a $50 restaurant bill. What percent tip is that?
Ireland has a 23% VAT (value-added tax, similar to a sales tax). How much will the VAT be on a purchase of a €250 item?
Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax), while employers paid another 6.2%.
1. How much will someone earning $45,000 a year pay towards social security out of their gross wages?
2. What is the total amount contributed towards the worker's social security?
A project on Kickstarter.com was aiming to raise $15,000 for a precision coffee press. They ended up with 714 supporters, raising 557% of their goal. How much did they raise?
Another project on Kickstarter for an iPad stylus raised 1,253% of their goal, raising a total of $313,490 from 7,511 supporters. What was their original goal?
The population of a town increased from 3,250 in 2008 to 4,300 in 2010. Find the absolute and relative (percent) increase.
The number of CDs sold in 2010 was 114 million, down from 147 million the previous year[1]. Find the absolute and relative (percent) decrease.
A company wants to decrease their energy use by at least 15%. If their next bill is $1,700 a month, were they successful? Why or why not?
A store is hoping an advertising campaign will increase their number of customers by at least 30%. They currently have about 80 customers a day.
1. How many customers will they have if their campaign is successful?
2. If they increase to 120 customers a day, were they successful? Why or why not?
An article reports “attendance dropped 6% this year, to 300.” What was the attendance before the drop?
An article reports “sales have grown by 30% this year, to $200 million.” What were sales before the growth?
The Walden University had 47,456 students in 2010, while Kaplan University had 77,966 students. Complete the following statements:
1. Kaplan’s enrollment was ___% larger than Walden’s.
2. Walden’s enrollment was ___% smaller than Kaplan’s.
3. Walden’s enrollment was ___% of Kaplan’s.
In the 2012 Olympics, Usain Bolt ran the 100m dash in 9.63 seconds. Jim Hines won the 1968 Olympic gold with a time of 9.95 seconds.
1. Bolt’s time was ___% faster than Hines’.
2. Hines’ time was ___% slower than Bolt’s.
3. Hines’ time was ___% of Bolt’s.
A store has clearance items that have been marked down by 60%. They are having a sale, advertising an additional 30% off clearance items. What percent of the original price do you end up paying?
Which is better: having a stock that goes up 30% on Monday than drops 30% on Tuesday, or a stock that drops 30% on Monday and goes up 30% on Tuesday? In each case, what is the net percent gain or loss?
Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?
1. “16.3% of Americans are without health insurance”[2]
2. “only 55.9% of adults receive employer provided health insurance”[3]
Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?
1. “We mark up the wholesale price by 33% to come up with the retail price”
2. “The store has a 25% profit margin”
Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?
1. “Every year since 1950, the number of American children gunned down has doubled.”
2. “The number of child gunshot deaths has doubled from 1950 to 1994.”
Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?[4]
1. “75 percent of the federal health care law’s taxes would be paid by those earning less than $120,000 a year”
2. “75 percent of those who would pay the penalty [health care law’s taxes] for not having insurance in 2016 would earn under $120,000”
Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?
1. “The school levy is only a 0.1% increase of the property tax rate.”
2. “This new levy is a 12% tax hike, raising our total rate to $9.33 per $1000 of value.”
A high school currently has a 30% dropout rate. They’ve been tasked to decrease that rate by 20%. Find the equivalent percentage point drop.
A politician’s support grew from 42% by 3 percentage points to 45%. What percent (relative) change is this?
Marcy has a 70% average in her class going into the final exam. She says "I need to get a 100% on this final so I can raise my score to 85%." Is she correct?
In a survey of households in the United States 9.4% of the households had 2 dogs. If there are about 117 million households in the U.S., about how many households have 2 dogs?
A typical 180-lb man is 111 lbs of water and 27 pounds of fat. What percent of the weight is water? What percent of the weight is fat?
Between the last two censuses, a town’s population grew from 3200 to 3650. What is the percent increase in the population?
In 1901 life expectancy at birth was 49 years. At the end of the century life expectancy at birth was 77 years. What is the increase in life expectancy during the 20^th century? Complete this sentence: Life expectancy in 2000 was ______ percent of life expectancy in 1901.
If you bought a stock for $250 and later sold it for $1250, by what percent did your stock increase in value? What percent of the purchase price was the sales price?
At work, you get a 2% cost-of-living adjustment (COLA). True of False: Over a 5-year period, your pay will increase by 10%. If this is false, by what percent will your pay increase over the 5-year period?
All merchandise at a store is on sale at 30% off. You have a coupon that gives you 10% off the purchase price. What will you pay for a jacket originally priced at $80? What percent off of the original price is your final price?
Your first three exam scores in a class are 74%, 89%, and 83%. What percent do you need to receive on the last exam to have an 85% overall in the class?
What is the markup percent for an item that has a wholesale price of $1.13 and a retail price of $1.69?
If you buy a refrigerator priced at $1325 and the sales tax rate is 6.5%, how much sales tax would you pay on the purchase? What would the total price of the refrigerator be?
Find the sales tax rate in a region where you paid $62.65 tax on a big screen TV priced at $895.
Why is this conclusion incorrect? “In a survey of a class, 70% want pizza for their class party and 20% want cake. Therefore, 90% want pizza or cake for their party.”
Why is this reasoning incorrect? “You received a score of 80% on five tests in a class and 90% on one test. Therefore, your average test score is 85% for the six tests.”
Suppose you have one quart of water/juice mix that is 50% juice, and you add 2 quarts of juice. What percent juice is the final mix?
During the 2004-2005 NBA, Kobe Bryant attempted 387 3-point shots and made 131 of them. Express his performance as a fraction, a decimal and a percent.

The following table describes the students enrolled at a small two-year college.

class	full-time	part-time
freshman	262	116
sophomore	214	239

What percent of the freshmen are full-time students?
What percent of the students are enrolled part-time?
What percent of the part-time students are sophomores?

Search

Text Color

Text Size

Margin Size

Font Type