AnswersWV-Algebra I CRWriting and Solving Equations in Two Variables

Writing and Solving Equations in Two Variables Answers

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Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation , where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies? (Round to the nearest cent, as needed.)

Question illustration
A
$1.75
B
$2.06
C
$2.39
D
$3.99
2
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Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of socks purchased, and let y represent the number of blouses purchased. Which equation models the purchases she made with $43.92?

A
x + y = 15.98
B
x + y = 43.92
C
43.92x - 2.99y = 12.99
D
2.99x + 12.99y = 43.92
3

Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation , where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies? (Round to the nearest cent, as needed.)

Question illustration
A
$1.75
B
$2.06
C
$2.39
D
$3.99
4

What is the value of x in the equation 2x + 3y = 36, when y = 6?

A
8
B
9
C
27
D
36
5

What is the value of x in the equation , when ?

Question illustration
A
4.6
B
8.4
C
10
D
12
6

What is the value of y in the equation 5x + 2y = 20, when x = 0.3?

A
2.5
B
2.8
C
9.25
D
10.75
7

What is the value of x in the equation 8x – 2y = 48, when y = 4?

A
6
B
7
C
14
D
48
8

What is the value of a in the equation , when ?

Question illustration
A
15
B
18
C
21
D
27
9

Which shows the correct solution of the equation, when ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of new-release and classic movies bought?

A
x = 8, y = 45
B
x = 10, y = 22
C
x = 16, y = 22
D
x = 18, y = 18
11

What is the value of y in the equation 5x + 2y = 20, when x = 0.3?

A
2.5
B
2.8
C
9.25
D
10.75
12

An isosceles triangle in which the two equal sides, labeled x, are longer than side y.

Question illustration
A
2 x minus 2.1 equals 7.5
Option A
B
4.2 plus y equals 7.5
Option B
C
y minus 4.2 equals 7.5
Option C
D
2.1 plus 2 x equals 7.5
Option D
13

What is the value of x in the equation x – y = 30, when y = 15?

Question illustration
A
4
B
8
C
80
D
200
14

Malik’s solution to the equation , when , is shown below. What error did Malik make first when solving the equation ?

Question illustration
A
Malik did not multiply correctly.
Option A
B
Malik added 240 to each side of the equation.
C
Malik did not multiply correctly.
Option C
D
Malik substituted 60 for y instead of x.
15

What is the value of m in the equation , when ?

Question illustration
A
20
B
32
C
44
D
48
16

What is the value of y in the equation 6.4x + 2.8y = 44.4, when x = 3?

A
y = 5
B
y = 6
C
y = 8
D
y = 9
17

Chin canned a number of quart jars and a number of pint jars of tomatoes from his garden. A pint is 16 ounces and a quart is 32 ounces. The number of pints he canned is represented by p, and the number of quarts he canned is represented by q. Which equation models the scenario if Chin canned a total of 1,280 ounces?

A
1280 plus 16 p equals 32 q
Option A
B
1280 plus 32 q equals 16 p
Option B
C
32 q minus 16 p equals 1280
Option C
D
16 p plus 32 q equals 1280
Option D
18

Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of socks purchased, and let y represent the number of blouses purchased. Which equation models the purchases she made with $43.92?

A
x + y = 15.98
B
x + y = 43.92
C
43.92x - 2.99y = 12.99
D
2.99x + 12.99y = 43.92
19

The perimeter of the scalene triangle is 54.6 cm.Which equation can be used to find the value of b if side a measures 8.7 cm?

Question illustration
A
8.7 plus b equals 54.6
Option A
B
17.4 plus b equals 54.6
Option B
C
26.1 plus b equals 54.6
Option C
D
34.8 plus b equals 54.6
Option D
20

Last month Maria hiked a total of 90 miles on two trails: a 5-mile mountain trail and a 10-mile canal trail. Let x represent the number of times Maria hiked the mountain trail, and let y represent the number of times Maria hiked the canal trail.Which equation can be used to find the number of times Maria hiked each trail?

A
x + y = 90
B
5x – 10y = 90
C
90 – 10y = 5x
D
90 + 10y = 5x

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