ElementaryAlgebra2e-WEB_3zxfu3Z-66

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112. The price of a share of
one stock rose from
$12.50 to $50. Find the
percent increase.
113. According to Time
magazine annual global
seafood consumption
rose from 22 pounds per
person in the 1960s to 38
pounds per person in
2011. Find the percent
increase. (Round to the
nearest tenth of a
percent.)
114. In one month, the median
home price in the
Northeast rose from
$225,400 to $241,500.
Find the percent increase.
(Round to the nearest
tenth of a percent.)
115. A grocery store reduced
the price of a loaf of
bread from $2.80 to
$2.73. Find the percent
decrease.
116. The price of a share of
one stock fell from $8.75
to $8.54. Find the percent
decrease.
117. Hernando’s salary was
$49,500 last year. This
year his salary was cut to
$44,055. Find the percent
decrease.
118. In 10 years, the
population of Detroit fell
from 950,000 to about
712,500. Find the percent
decrease.
119. In 1 month, the median
home price in the West
fell from $203,400 to
$192,300. Find the
percent decrease. (Round
to the nearest tenth of a
percent.)
120. Sales of video games and
consoles fell from $1,150
million to $1,030 million
in 1 year. Find the percent
decrease. (Round to the
nearest tenth of a
percent.)
Solve Simple Interest Applications
In the following exercises, solve.
121. Casey deposited $1,450 in
a bank account with
interest rate 4%. How
much interest was earned
in two years?
122. Terrence deposited
$5,720 in a bank account
with interest rate 6%. How
much interest was earned
in 4 years?
123. Robin deposited $31,000
in a bank account with
interest rate 5.2%. How
much interest was earned
in 3 years?
124. Carleen deposited
$16,400 in a bank account
with interest rate 3.9%.
How much interest was
earned in 8 years?
125. Hilaria borrowed $8,000
from her grandfather to
pay for college. Five years
later, she paid him back
the $8,000, plus $1,200
interest. What was the
rate of interest?
126. Kenneth loaned his niece
$1,200 to buy a computer.
Two years later, she paid
him back the $1,200, plus
$96 interest. What was
the rate of interest?
127. Lebron loaned his
daughter $20,000 to help
her buy a condominium.
When she sold the
condominium four years
later, she paid him the
$20,000, plus $3,000
interest. What was the
rate of interest?
128. Pablo borrowed $50,000
to start a business. Three
years later, he repaid the
$50,000, plus $9,375
interest. What was the
rate of interest?
129. In 10 years, a bank
account that paid 5.25%
earned $18,375 interest.
What was the principal of
the account?
130. In 25 years, a bond that
paid 4.75% earned $2,375
interest. What was the
principal of the bond?
131. Joshua’s computer loan
statement said he would
pay $1,244.34 in interest
for a 3-year loan at 12.4%.
How much did Joshua
borrow to buy the
computer?
132. Margaret’s car loan
statement said she would
pay $7,683.20 in interest
for a 5-year loan at 9.8%.
How much did Margaret
borrow to buy the car?
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Solve Applications with Discount or Mark-up
In the following exercises, find the sale price.
133. Perla bought a cell phone
that was on sale for $50
off. The original price of
the cell phone was $189.
134. Sophie saw a dress she
liked on sale for $15 off.
The original price of the
dress was $96.
135. Rick wants to buy a tool
set with original price
$165. Next week the tool
set will be on sale for $40
off.
136. Angelo’s store is having a
sale on televisions. One
television, with original
price $859, is selling for
$125 off.
In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.
137. Janelle bought a beach
chair on sale at 60% off.
The original price was
$44.95.
138. Errol bought a skateboard
helmet on sale at 40% off.
The original price was
$49.95.
139. Kathy wants to buy a
camera that lists for $389.
The camera is on sale
with a 33% discount.
140. Colleen bought a suit that
was discounted 25% from
an original price of $245.
141. Erys bought a treadmill
on sale at 35% off. The
original price was $949.95
(round to the nearest
cent.)
142. Jay bought a guitar on
sale at 45% off. The
original price was $514.75
(round to the nearest
cent.)
In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a
percent if needed.)
143. Larry and Donna bought
a sofa at the sale price of
$1,344. The original price
of the sofa was $1,920.
144. Hiroshi bought a
lawnmower at the sale
price of $240. The original
price of the lawnmower is
$300.
145. Patty bought a baby
stroller on sale for
$301.75. The original
price of the stroller was
$355.
146. Bill found a book he
wanted on sale for
$20.80. The original price
of the book was $32.
147. Nikki bought a patio set
on sale for $480. The
original price was $850.
To the nearest tenth of a
percent, what was the
rate of discount?
148. Stella bought a dinette set
on sale for $725. The
original price was $1,299.
To the nearest tenth of a
percent, what was the
rate of discount?
In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.
149. Daria bought a bracelet at
original cost $16 to sell in
her handicraft store. She
marked the price up 45%.
150. Regina bought a
handmade quilt at
original cost $120 to sell
in her quilt store. She
marked the price up 55%.
151. Tom paid $0.60 a pound
for tomatoes to sell at his
produce store. He added
a 33% mark-up.
152. Flora paid her supplier
$0.74 a stem for roses to
sell at her flower shop.
She added an 85% mark-
up.
153. Alan bought a used
bicycle for $115. After re-
conditioning it, he added
225% mark-up and then
advertised it for sale.
154. Michael bought a classic
car for $8,500. He
restored it, then added
150% mark-up before
advertising it for sale.
3.2 • Solve Percent Applications 317
Everyday Math
155. Leaving a Tip At the campus coffee cart, a
medium coffee costs $1.65. MaryAnne brings
$2.00 with her when she buys a cup of coffee
and leaves the change as a tip. What percent tip
does she leave?
156. Splitting a Bill Four friends went out to lunch
and the bill came to $53.75. They decided to add
enough tip to make a total of $64, so that they
could easily split the bill evenly among
themselves. What percent tip did they leave?
Writing Exercises
157. Without solving the problem “44 is 80% of what
number” think about what the solution might be.
Should it be a number that is greater than 44 or
less than 44? Explain your reasoning.
158. Without solving the problem “What is 20% of
300?” think about what the solution might be.
Should it be a number that is greater than 300 or
less than 300? Explain your reasoning.
159. After returning from vacation, Alex said he
should have packed 50% fewer shorts and 200%
more shirts. Explain what Alex meant.
160. Because of road construction in one city,
commuters were advised to plan that their
Monday morning commute would take 150% of
their usual commuting time. Explain what this
means.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ After reviewing this checklist, what will you do to become confident for all goals?
3.3 Solve Mixture Applications
Learning Objectives
By the end of this section, you will be able to:
Solve coin word problems
Solve ticket and stamp word problems
Solve mixture word problems
Use the mixture model to solve investment problems using simple interest
BE PREPARED 3.9 Before you get started, take this readiness quiz.
Multiply: 14(0.25).
If you missed this problem, review Example 1.97.
BE PREPARED 3.10 Solve:
If you missed this problem, review Example 2.44.
BE PREPARED 3.11 The number of dimes is three more than the number of quarters. Let q represent the
number of quarters. Write an expression for the number of dimes.
If you missed this problem, review Example 1.26.
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Solve Coin Word Problems
In mixture problems, we will have two or more items with different values to combine together.The mixture model is
used by grocers and bartenders to make sure they set fair prices for the products they sell. Many other professionals,
like chemists, investment bankers, and landscapers also use the mixture model.
MANIPULATIVE MATHEMATICS
Doing the Manipulative Mathematics activity Coin Lab will help you develop a better understanding of mixture word
problems.
We will start by looking at an application everyone is familiar with—money!
Imagine that we take a handful of coins from a pocket or purse and place them on a desk. How would we determine the
value of that pile of coins? If we can form a step-by-step plan for finding the total value of the coins, it will help us as we
begin solving coin word problems.
So what would we do? To get some order to the mess of coins, we could separate the coins into piles according to their
value. Quarters would go with quarters, dimes with dimes, nickels with nickels, and so on. To get the total value of all the
coins, we would add the total value of each pile.
How would we determine the value of each pile? Think about the dime pile—how much is it worth? If we count the
number of dimes, we’ll know how many we have—the number of dimes.
But this does not tell us the value of all the dimes. Say we counted 17 dimes, how much are they worth? Each dime is
worth $0.10—that is the value of one dime. To find the total value of the pile of 17 dimes, multiply 17 by $0.10 to get
$1.70. This is the total value of all 17 dimes. This method leads to the following model.
Total Value of Coins
For the same type of coin, the total value of a number of coins is found by using the model
where
number is the number of coins
value is the value of each coin
total value is the total value of all the coins
The number of dimes times the value of each dime equals the total value of the dimes.
We could continue this process for each type of coin, and then we would know the total value of each type of coin. To get
the total value of all the coins, add the total value of each type of coin.
Let’s look at a specific case. Suppose there are 14 quarters, 17 dimes, 21 nickels, and 39 pennies.
3.3 • Solve Mixture Applications 319
The total value of all the coins is $6.64.
Notice how the chart helps organize all the information! Let’s see how we use this method to solve a coin word problem.
EXAMPLE 3.26
Adalberto has $2.25 in dimes and nickels in his pocket. He has nine more nickels than dimes. How many of each type of
coin does he have?
Solution
Step 1. Read the problem. Make sure all the words and ideas are understood.
• Determine the types of coins involved.
Think about the strategy we used to find the value of the handful of coins. The first thing we need is to notice what
types of coins are involved. Adalberto has dimes and nickels.
• Create a table to organize the information. See chart below.
◦ Label the columns “type,” “number,” “value,” “total value.”
◦ List the types of coins.
◦ Write in the value of each type of coin.
◦ Write in the total value of all the coins.
We can work this problem all in cents or in dollars. Here we will do it in dollars and put in the dollar sign ($) in the
table as a reminder.
The value of a dime is $0.10 and the value of a nickel is $0.05. The total value of all the coins is $2.25. The table
below shows this information.
Step 2. Identify what we are looking for.
• We are asked to find the number of dimes and nickels Adalberto has.
Step 3. Name what we are looking for. Choose a variable to represent that quantity.
• Use variable expressions to represent the number of each type of coin and write them in the table.
• Multiply the number times the value to get the total value of each type of coin.
Next we counted the number of each type of coin. In this problem we cannot count each type of coin—that is what you
are looking for—but we have a clue. There are nine more nickels than dimes. The number of nickels is nine more than
the number of dimes.
Fill in the “number” column in the table to help get everything organized.
Now we have all the information we need from the problem!
320 3 • Math Models
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	Chapter 3 Math Models
	3.3 Solve Mixture Applications