Lesson 3.3: Modeling with Systems of Linear Equations Answers

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11

A business owner pays $1,200 per month in rent and a total of $120 per hour in employee salary for each hour the store is open. On average, the store brings in $200 in net sales per hour.Which equations can be solved to determine the break-even point if C(x) represents the cost function, R(x) represents the revenue function, and x the number of hours per month the store is open?

A
C(x) = 1,200+120x; R(x) = 200x
B
C(x) = 1,200+120; R(x) = 200x
C
C(x) = 200x; R(x) = 1,200+120x
D
C(x) = 200x; R(x) = 1,200+120
12

Adele is 5 years older than Timothy. In three years, Timothy will be of Adele’s age. What is Adele’s current age?

Answer not available
13

A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink receipts totaled $360, and 4 times as many cold beverages were sold as hot beverages.Which system of linear equations represents the beverage sales on Saturday?

A
4c = h1.5c + 2h = 360
B
c = 4h1.5c + 2h = 360
C
c + h = 3601.5c = 4(2h)
D
c + h = 3604(1.5c) = 2h
14

Each month, Kaisorn deposits $50.00 onto her public transportation card. It costs her $2.50 per trip to ride the subway. Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway.If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs?

A
50 − 2.5x = y 40 − 2x = y
B
50 + 2.5x = y 40 + 2x = y
C
50 − 2.5y = x 40 − 2y = x
D
50 + 2.5y = x 40 + 2y = x
15

Micah rows his boat on a river 4.48 miles downstream, with the current, in 0.32 hours. He rows back upstream the same distance, against the current, in 0.56 hours. Assuming his rowing speed and the speed of the current are constant, what is the speed of the current?

A
3 miles per hour
B
8 miles per hour
C
11 miles per hour
D
14 miles per hour
16

A motorboat travels 9 miles downstream (with the current) in 30 minutes. The return trip upstream (against the current) takes 90 minutes.Which system of equations can be used to find x, the speed of the boat in miles per hour, and y, the speed of the current in miles per hour? Recall the formula d = rt.

A
9 = 0.5(x – y) 9 = 1.5(x + y)
B
9 = 1.5(x – y) 9 = 0.5(x + y)
C
0.5 = 9(x – y) 1.5 = 9(x + y)
D
1.5 = 9(x – y) 0.5 = 9(x + y)
17

A pilot flew a 400-mile flight in 2.5 hours flying into the wind. Flying the same rate and with the same wind speed, the return trip took only 2 hours, with a tailwind.What was the speed of the wind?

A
20
B
40
C
160
D
180
18

Nina is 10 years younger than Deepak. Deepak is 3 times as old as Nina. Which system of equations can be used to find d, Deepak's age, and n, Nina's age?

A
d = n + 10 d = 3n
B
d = n − 10 d = 3n
C
d = n + 10 n = 3d
D
d = n − 10 n = 3d
19

Yolanda paid for her movie ticket using 28 coins, all nickels and quarters. The ticket cost $4. Which system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, Yolanda used?

A
n + q = 28 0.05n + 0.25q = 4
B
n + q = 4 5n + 25q = 28
C
n + q = 28 5n + 25q = 4
D
n + q = 4 0.05n + 0.25q = 28
20

The hardcover version of a book weighs twice as much as its paperback version. The hardcover book and the paperback together weigh 4.2 pounds. Which system of equations can be used to find h, the weight of the hardcover book, and p, the weight of the paperback?

A
h = p − 4.2 h = 2p
B
h = 4.2 − p p = 2h
C
h = p − 4.2 p = 2h
D
h = 4.2 − p h = 2p

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