Homework 2 - Section 2.3 #5
Intermediate Algebra / MAT 135 Fall 2016 possible master (Prof. Fleischner)
Student Name/ID:
1. Translate this phrase into an algebraic expression.
Six more than the product of 12 and Victor's score
Use the variable v to represent Victor's score.
2. Translate this phrase into an algebraic expression.
23 increased by twice a number
Use the variable n to represent the unknown number.
3. Translate the sentence into an equation.
The difference of a number times 7 and 9 is equal to 3 .
Use the variable x for the unknown number.
4. Translate the sentence into an equation.
Four times the difference of a number and 9 is equal to 8 .
Use the variable x for the unknown number.
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5. Hong needs to memorize words on a vocabulary list for French class. He has memorized 12 of
the words, which is two-thirds of the list. How many words are on the list?
6. Abdul is on his way home in his car. He has driven 30 miles so far, which is five-sixths of the way
home. What is the total length of his drive?
7. On Sunday, a local hamburger shop sold a combined total of 420 hamburgers and
cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold.
How many hamburgers were sold on Sunday?
8. A washer and a dryer cost $804 combined. The washer costs $96 less than the dryer. What is
the cost of the dryer?
9. Hong rented a truck for one day. There was a base fee of $16.99 , and there was an additional
charge of 94 cents for each mile driven. Hong had to pay $267.97 when he returned the truck. For
how many miles did he drive the truck?
10. Leila purchased a prepaid phone card for $25 . Long distance calls cost 23 cents a minute using
this card. Leila used her card only once to make a long distance call. If the remaining credit on her
card is $14.65 , how many minutes did her call last?
11. The sum of three numbers is 106 . The third number is 2 times the first. The second number is
10 more than the first. What are the numbers?
12. The sum of three numbers is 75 . The second number is 5 less than the first. The third number is
3 times the first. What are the numbers?
81
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13. Three consecutive integers have a sum of 81 . Find the integers.
14. Three consecutive integers have a sum of 54 . Find the integers.
15. Lisa has a job transporting soft drinks by truck. Her truck is filled with cans that weigh 14 ounces
each and bottles that weigh 70 ounces each. There is a combined total of 860 cans and bottles in
her truck.
Let x be the number of 14 -ounce cans in her truck. Write an expression for the combined total
weight (in ounces) of the cans and bottles in her truck.
16. Rachel has a job transporting soft drinks by truck. Her truck is filled with cans that weigh 14
ounces each and bottles that weigh 70 ounces each. There is a combined total of 870 cans and
bottles in her truck.
Let x be the number of 14 -ounce cans in her truck. Write an expression for the combined total
weight (in ounces) of the cans and bottles in her truck.
17. Rueben's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee
costs Rueben $4.30 per pound, and type B coffee costs $5.55 per pound. This month's blend used
three times as many pounds of type B coffee as type A, for a total cost of $481.85 . How many
pounds of type A coffee were used?
18. At the city museum, child admission is $5.30 and adult admission is $8.80 . On Wednesday,
154 tickets were sold for a total sales of $1050.70 . How many adult tickets were sold that day?
240
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19. Two trains leave stations 240 miles apart at the same time and travel toward each other. One
train travels at 70 miles per hour while the other travels at 80 miles per hour. How long will it take for
the two trains to meet?
Do not do any rounding.
hours
20. Two trains leave the station at the same time, one heading west and the other east. The
westbound train travels at 115 miles per hour. The eastbound train travels at 95 miles per hour.
How long will it take for the two trains to be 336 miles apart?
Do not do any rounding.
hours
21. The length of a rectangle is six times its width.
2
If the area of the rectangle is 216 ft , find its perimeter.
22. The length of a rectangle is 4 yd longer than its width.
If the perimeter of the rectangle is 40 yd , find its area.
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23. Last year, Leila invested her money in two purchases. She purchased a certificate of deposit for
$2000 that paid 2% interest per year and purchased $3000 in corporate bonds paying 6% interest
per year.
Answer the questions below. Do not do any rounding.
(a) What was the total interest earned at the end of 1 year?
$ _____
(b) What was the percent interest for her total investment?
_____ %
24. Last year, Tammy invested her money in two purchases. She purchased a certificate of deposit
for $7000 that paid 11 % interest per year and purchased $1000 in corporate bonds paying 5%
interest per year.
Answer the questions below. Do not do any rounding.
(a) What was the total interest earned at the end of 1 year?
$ _____
(b) What was the percent interest for her total investment?
_____ %
25. Two factory plants are making TV panels. Yesterday, Plant A produced 4000 fewer panels than
Plant B did. Three percent of the panels from Plant A and 5% of the panels from Plant B were
defective. How many panels did Plant A produce, if the two plants together produced 1320
defective panels?
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26. Rachel invested her savings in two investment funds. The amount she invested in Fund A was 4
times as much as the amount she invested in Fund B. Fund A returned a 6% profit and Fund B
returned a 5% profit. How much did she invest in Fund B, if the total profit from the two funds
together was $3480 ?
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Homework 2 - Section 2.3 #5 Answers for class Intermediate
Algebra / MAT 135 Fall 2016 possible master
1. 12 v + 6
2. 23 + 2 n
3. 7 x − 9 = 3
4. 4 x − 9 = 8
5. 18 words
6. 36 miles
7. 105 hamburgers
8. $450
9. 267 miles
10. 45 minutes
11. First number:
24
Second number:
34
Third number:
48
12. First number:
16
Second number:
11
Third number:
48
13. 26 , 27 , 28
14. 17 , 18 , 19
= −56 + 60,200
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15. total weight (in ounces) = −56 x + 60,200
16. total weight (in ounces) = −56 x + 60,900
17. 23 pounds
18. 67 tickets
19. 1.6 hours
20. 1.6 hours
21. 84 ft
22. 96 yd 2
23.
(a) What was the total interest earned at the end of 1 year?
$220
(b) What was the percent interest for her total investment?
4.4 %
24.
(a) What was the total interest earned at the end of 1 year?
$820
(b) What was the percent interest for her total investment?
10.25 %
25. Number of panels produced by Plant A: 14,000
26. Amount invested in Fund B: $12,000
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