Elementary and Intermediate Algebra 5th

Alan S. Tussy, R. David Gustafson

Chapter 2

Equations, Inequalities, and Problem Solving - all with Video Answers

Educators

Section 6

More about Problem Solving

Problem 1

Fill in the blanks.
Problems that involve depositing money are called ______ problems, and problems that involve moving vehicles are called uniform ______ problems.

Alanya H.

Alanya H.

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Problem 2

Problems that involve combining ingredients are called ______ problems, and problems that involve collections of different items having different values are called ______.

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Problem 3

Complete only the principal column given that part of 30,000 dollar is invested in stocks and the rest in art.
(TABLE CAN'T COPY)

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Problem 4

A man made two investments that earned a combined annual simple interest of 280 dollar. Complete the table and then form an equation for this investment problem.
(TABLE CAN'T COPY)

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Problem 5

Complete only the rate column given that the east-bound plane flew $150 \mathrm{mph}$ slower than the west-bound plane.
(TABLE CAN'T COPY)

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Problem 6

a. Complete only the time column given that a runner wants to overtake a walker and the walker had a $\frac{1}{2}$ -hour head start.
b. Complete only the time column given that part of a 6 -hour drive was in fog and the other part was in clear conditions.
(TABLE CAN'T COPY)

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Problem 7

A husband and wife drive in opposite directions to work. Their drives last the same amount of time and their
workplaces are 80 miles apart. Complete the table and then form an equation for this distance problem.
(TABLE CAN'T COPY)

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Problem 8

a. How many gallons of acetic acid are there in barrel $2 ?$
b. Suppose the contents of the two barrels are poured into an
empty third barrel. How many gallons of liquid will the third barrel contain?
c. Estimate the strength of the solution in the third barrel: $15 \%,$ $35 \%,$ or $60 \%$ acid?
(IMAGE CAN'T COPY)

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Problem 9

a. Two antifreeze solutions are combined to form a mixture. Complete the table and then form an equation for this mixture problem.
b. Two oil-and-vinegar salad dressings are combined to make a new mixture. Complete the table and then form an equation for this mixture problem.
(TABLE CAN'T COPY)

Alanya H.

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Problem 10

The value of all the nylon brushes that a paint store carries is $\$ 670 .$ Complete the table and then form an equation for this number-value problem.
(TABLE CAN'T COPY)

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Problem 11

Write $6 \%$ and $15.2 \%$ in decimal form.

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Problem 12

By what power of 10 should each decimal be multiplied to make it a whole number?

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Problem 13

Solve each equation.
$0.18 x+0.45(12-x)=0.36(12)$

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Problem 14

Solve each equation.
$0.12 x+0.20(4-x)=0.6$

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Problem 15

Solve each equation.
$0.08 x+0.07(15,000-x)=1,110$

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Problem 16

Solve each equation.
$0.108 x+0.07(16,000-x)=1,500$

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Problem 17

Investment problems.
The financial board of a corporation invested 25,000 dollar overseas, part at 4% and part at 7$ annual simple interest. Find the amount invested at each rate if the first year combined income from the two investments was 1,300 dollar.

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Problem 18

Investment problems.
A credit union loaned out 50,000 dollar, part at an annual simple rate of 5% and the rest at an annual simple rate of 8%.They collected combined interest of 3,400 dollar from the loans that year. How much was loaned out at each rate?

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Problem 19

Investment problems.
A salesperson used her 3,500 dollar year-end bonus to purchase some old gold and silver coins. She earned 15% annual simple interest on the gold coins and 12% annual simple interest on the silver coins. If she saw a return on her investment of 480 dollar the first year, how much did she invest in
each type of coin?

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Problem 20

Investment problems.
An investment club used funds totaling 200,000 dollar to invest in a bio-tech company and in an ethanol plant, with hopes of earning 11% and 14% annul simple interest, respectively. Their hunch paid off. The club made a total of 24,250 dollar interest the first year. How much was invested at each rate?

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Problem 21

Investment problems.
A professor wants to supplement her pension with investment interest. If she invests 28,000 dollar at 6% annual simple interest, how much would she have to invest at 7% annual simple interest to achieve a goal of 3,500 dollar per year in supplemental income?

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Problem 22

Investment problems.
An investor wants to receive 1,000 dollar annually from two investments. He has put 4,500 dollar in a money market account paying 4% annual simple interest. How much should he invest in a stock fund that pays 10% annual simple interest to achieve his goal?

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Problem 23

Investment problems.
The form below shows the interest income Terrell Washington earned in 2011 from two savings accounts. He deposited a total of 15,000 dollar at the first of that year, and made no further deposits or withdrawals. How much money did he deposit in account 822 and in account 721 dollar?

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Problem 24

Investment problems.
A financial planner recommends a plan for a client who has $\$ 65,000$ to invest. (See the chart at the right.) At the end of the presentation, the client asks, "How much will be invested at each rate?" Answer this question using the given information.

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Problem 25

Investment problems.
Equal amounts are invested in each of three accounts paying 7%, 8%, and 10.5% annual simple interest. If one year's combined interest income is 1,249.50 dollar, how much is invested in each account?

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Problem 26

Investment problems.
Maggy lent her brother some money at $2 \%$ annual simple interest. She lent her sister twice as much money at half of the interest rate. In one year, Maggy collected combined interest of $\$ 200$ from her brother and sister. How much did she lend each of them?

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Problem 27

Investment problems.
A newly hired MBA graduate received an 18,000 dollar signing bonus from her employer. She invested part of it in a credit union account earning 3% annual simple interest and the rest in utility stocks that suffered a 7% loss of value. The net income from both investments for the first year was only 90 dollar. How much of her bonus was originally placed in each investment?

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Problem 28

Investment problems.
A financial planner invested a portion of his client's 190,000 dollar in a high-yield mutual fund that earned 11% dollar annual simple interest. The remainder of the money was invested in a mini-mall development. Unfortunately, that investment lost 25% of its value the first year. Find the amount originally made in each investment if the first-year net income was 6,500 dollar.

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Problem 29

Uniform motion problems.
During a storm, two teams of scientists leave a university at the same time in vans to search for tornadoes. The first team travels east at $20 \mathrm{mph}$ and the second travels west at $25 \mathrm{mph}$. If their radios have a range of up to 90 miles, how long will it be before they lose radio contact?

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Problem 30

Uniform motion problems.
Two remotely controlled unmanned aircraft are launched in opposite directions. One flies east at 78 mph and the other west at $82 \mathrm{mph}$. How long will it take the aircraft to fly a combined distance of 560 miles?

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Problem 31

Uniform motion problems.
A husband and wife work different shifts at the same plant. When the husband leaves from work to make the 20-mile trip home, the wife leaves their home and drives to work. They travel on the same road. The husband's driving rate is 45 mph and the wife's is 35 mph. How long into their drives can they wave at each other when passing on the road?

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Problem 32

Uniform motion problems.
An airliner leaves Berlin, Germany, headed for Montreal, Canada, flying at an average speed of 450 mph. At the same time, an airliner leaves Montreal headed for Berlin, averaging 500 mph. If the airports are 3, 800 miles apart, when will the air traffic controllers have to make the pilots aware that the planes are passing each other?

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Problem 33

Uniform motion problems.
A cyclist leaves his training base for a morning workout, riding at the rate of $18 \mathrm{mph}$. One and one-half hours later, his support staff leaves the base in a car going $45 \mathrm{mph}$ in the same direction. How long will it take the support staff to catch up with the cyclist?

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Problem 34

Uniform motion problems.
How long will it take a mother, running at 4 feet per second, to catch up with her toddler, running down the sidewalk at 2 feet per second, if the child had a 5 -second head start?

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Problem 35

Uniform motion problems.
A car averaged $40 \mathrm{mph}$ for part of a trip and 50
mph for the remainder. If the 5 -hour trip covered 210 miles, for
how long did the car average $40 \mathrm{mph} ?$

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Problem 36

Uniform motion problems.
An athlete runs up a set of stadium stairs at a
rate of 2 stairs per second, immediately turns around, and then
descends the same stairs at a rate of 3 stairs per second. If the
workout takes 90 seconds, how long does it take him to run up
the stairs?

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Problem 37

Uniform motion problems.
A trucker drove for 4 hours before he encountered icy road conditions. He reduced his speed by 20
mph and continued driving for 3 more hours. Find his average speed during the first part of the trip if the entire trip was 325 miles.

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Problem 38

Uniform motion problems.
Two trains are 330 miles apart, and their speeds differ by 20 mph. Find the speed of each train if they
are traveling toward each other and will meet in 3 hours.

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Problem 39

Liquid mixture problems.
How many gallons of a $3 \%$ salt solution must
be mixed with 50 gallons of a $7 \%$ solution to obtain a $5 \%$
solution?

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Problem 40

Liquid mixture problems.
A photographer wishes to $\operatorname{mix} 2$ liters of a $5 \%$
acetic acid solution with a $10 \%$ solution to get a $7 \%$ solution.
How many liters of $10 \%$ solution must be added?

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Problem 41

To make low-fat cottage cheese, milk
containing 4 $\%$ butterfat is mixed with milk containing $1 \%$
butterfat to obtain 15 gallons of a mixture containing $2 \%$
butterfat. How many gallons of each milk must be used?

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Problem 42

Liquid mixture problems.
How many quarts of a $10 \%$ antifreeze solution
must be mixed with 16 quarts of a $40 \%$ antifreeze solution to
make a $30 \%$ solution?

Alanya H.

Numerade Educator

Problem 43

Liquid mixture problems.
A printer has ink that is $8 \%$ cobalt blue color and ink
that is $22 \%$ cobalt blue color. How many ounces of each ink are
needed to make one-half gallon ( 64 ounces) of ink that is
$15 \%$ cobalt blue color?

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Problem 44

Liquid mixture problems.
One website recommends a $6 \%$ chlorine
bleach-water solution to remove mildew. A chemical lab has
$3 \%$ and $15 \%$ chlorine bleach-water solutions in stock. How
many gallons of each should be mixed to obtain 100 gallons of
the mildew spray?

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Problem 45

Liquid mixture problems.
The colors on the paint chip card below
are created by adding different amounts of orange tint to a
white latex base. How many gallons of Desert Sunrise should
be mixed with 1 gallon of Bright Pumpkin to obtain Cool
Cantaloupe?

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Problem 46

Liquid mixture problems.
A nurse wants to add water to 30 ounces of a
$10 \%$ solution of benzalkonium chloride to dilute it to an
$8 \%$ solution. How much water must she add? (Hint: Water is
$0 \%$ benzalkonium chloride.)

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Problem 47

Dry mixture problems.
A store sells bluegrass seed for $\$ 6$ per pound and ryegrass seed for 3 dollar per pound. How much ryegrass must be mixed with 100 pounds of bluegrass to obtain a blend that will
sell for 5 dollar per pound?

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Problem 48

Dry mixture problems.
A store sells regular coffee for 8 dollar a pound and gourmet coffee for 4 dollar a pound. To get rid of 40 pounds of the gourmet coffee, a shopkeeper makes a blend to put on sale for 10 dollar a pound. How many pounds of regular coffee should he use?

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Problem 49

Dry mixture problems.
How many scoops of natural seedless raisins costing 3.45 dollar per scoop must be mixed with 20 scoops of golden seedless raisins costing 2.55 dollar per scoop to obtain a mixture costing 3 dollar per scoop?

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Problem 50

Dry mixture problems.
Fertilizer with weed control costing 38 dollar per 50- pound bag is to be mixed with a less expensive fertilizer costing 6 dollar per 50 -pound bag to make 16 bags of fertilizer that can be sold for 28 dollar per bag. How many bags of cheaper fertilizer should be used?

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Problem 51

Dry mixture problems.
How many 10 -ounce bags of Romaine lettuce
must be mixed with fifty 10 -ounce bags of Iceberg lettuce to
obtain a blend that sells for 2.50 dollar per ten-ounce bag?

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Problem 52

Dry mixture problems.
Lemon drops worth 3.80 dollar per pound are to be mixed with jelly beans that cost 2.40 dollar per pound to make 300 pounds of a mixture worth 2.96 dollar per pound. How many pounds of each candy should be used?

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Problem 53

Dry mixture problems.
A pound of tin is worth 1 dollar more than a pound of
copper. Four pounds of tin are mixed with 6 pounds of copper
to make bronze that sells for 3.65 dollar per pound. How much is a
pound of tin worth?

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Problem 54

Dry mixture problems.
A bag of peanuts is worth 0.30 dollar less than a bag
of cashews. Equal amounts of peanuts and cashews are used to
make 40 bags of a mixture that sells for 1.05 per bag. How
much is a bag of cashews worth?

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Problem 55

The owners of an apartment building rent equal numbers of $1-, 2-,$ and 3 -bedroom units. The monthly rent for a 1-bedroom is $\$ 550,$ a 2 -bedroom is $\$ 700,$ and a 3 -bedroom is $\$ 900 .$ If the total monthly income is $\$ 36,550,$ how many of each type of unit are there?

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Problem 56

A store warehouses 40 more portables than bigscreen TV sets, and 15 more consoles than big-screen sets. The monthly storage cost for a portable is $\$ 1.50,$ a console is $\$ 4.00,$ and a big-screen is $\$ 7.50 .$ If storage for all the televisions costs $\$ 276$ per month, how many big-screen sets are in stock?

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Problem 57

Dry mixture problems.
Three software applications are priced as shown. Spreadsheet and database programs sold in equal numbers, but 15 more word processing applications were sold than the other two combined. If the three applications generated sales of 72,000 dollar, how many spreadsheets were sold?

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Problem 58

Dry mixture problems.
With summer approaching, the number of air conditioners sold is expected to be double that of stoves and refrigerators combined. Stoves sell for 350 dollar, refrigerators for
450 dollar, and air conditioners for 500 dollar, and sales of 56,000 dollar are expected. If stoves and refrigerators sell in equal numbers, how many of each appliance should be stocked?

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Numerade Educator

Problem 59

Dry mixture problems.
When a child emptied his coin bank, he had a
collection of pennies, nickels, and dimes. There were 20 more
pennies than dimes and the number of nickels was triple the
number of dimes. If the coins had a value of 5.40 dollar, how many
of each type coin were in the bank?

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Problem 60

Dry mixture problems.
A scuba diver, hired by an amusement park,
collected 121 dollar in nickels, dimes, and quarters at the bottom of
a wishing well. There were 500 nickels, and 90 more quarters
than dimes. How many quarters and dimes were thrown into
the wishing well?

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Problem 61

Dry mixture problems.
Epiphanny Prince, of New York, scored 113 points
in a high school game on February $1,2006,$ breaking a national
prep record that was held by Cheryl Miller. Prince made 46
more 2 -point baskets than 3 -point baskets, and only 1 free
throw. How many 2 -point and 3 -point baskets did she make?

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Problem 62

Dry mixture problems.
Museum Tours. The ticket prices for the Coca-Cola Museum
in Atlanta are shown. A family purchased 3 more children's
tickets than adult tickets, and 1 less senior ticket than adult
tickets. The total cost of the tickets was $\$ 131 .$ How many of
each type did they purchase?

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Problem 63

Create a mixture problem of your own, and solve it.

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Problem 64

Write an investment problem to fit the following equation, and
then solve it.
$$
0.08 x+0.07(10,000-x)=770
$$

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Problem 65

Explain the error in each statement.
a. If 3 pounds of Mocha coffee are mixed with $x$ pounds of
Java coffee, there will be $3 x$ pounds of the Mocha-Java
blend.
b. A financial manager has a total of 5,000 dollar to invest in two
accounts. If $S x$ is invested in the first account, then
$\$(x-5,000)$ is left to be invested in the second account.

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Problem 66

Is it possible to $\operatorname{mix}$ a $10 \%$ sugar solution with a $20 \%$ sugar
solution to get a $30 \%$ sugar solution? Explain.

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Problem 67

Multiply.
$$
-12(3 a+4 b-32)
$$

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Problem 68

Multiply.
$$
\frac{1}{2}(4 b-8)
$$

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Problem 69

Multiply.
$$
3(5 t+1) 2
$$

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Problem 70

Multiply.
$$
2.9(4 c-12)
$$

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Problem 71

How much water must be boiled away to
increase the concentration of 300 milliliters of a 2\% salt
solution to a 3 $\%$ salt solution?

Check back soon!

Problem 72

How much water should be added to 20
ounces of a $15 \%$ solution of alcohol to dilute it to a $10 \%$
alcohol solution?

Alanya H.

Numerade Educator

Problem 73

A plumber has a choice of two investment plans:
An insured fund that pays $11 \%$ interest A risky investment that pays a $13 \%$ return If the same amount invested at the higher rate would generate an extra $\$ 150$ per year, how much does the plumber have to invest?

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Problem 74

The amount of annual interest earned by 8,000 dollar
invested at a certain rate is 200 dollar less than 12,000 dollar would earn
at a rate 1% lower. At what rate is the 8,000 dollar invested?

Alanya H.

Numerade Educator