Modeling with Systems of Linear Equations Answers

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Lily sold 18 items at the street fair. She sold bracelets for $6 each and necklaces for $5 each for a total of $101. Which system of equations can be used to find b, the number of bracelets she sold, and n, the number of necklaces she sold?

A
b + n = 101 6b + 5n = 18
B
b + n = 101 5b + 6n = 18
C
b + n = 18 6b + 5n = 101
D
b + n = 18 5b + 6n = 101
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An aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour.Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? Recall the formula d = rt.

A
0.75(x + y) = 120 x − y = 120
B
0.75(x − y)= 120 x + y = 120
C
120(x + y) = 0.75 120(x − y) = 1
D
120(x − y) = 0.75 120(x + y) = 1
4

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
5

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)
6

Zorah, a musician, pays $120 to have her instrument tuned and $10 per hour for a booth at a fair. She estimates that she earns $25 per hour in tips. The equation can be used to represent the break-even point.120 + 10x = 25xHow many hours, x, will Zorah have to play in order to break even?

A
4
B
5
C
8
D
12
7

Bethany has $3.10 in nickels and dimes. She has a total of 44 coins. What is the value of the nickels Bethany has?

A
$0.90
B
$1.30
C
$1.80
D
$2.60
8

At his new job, Jeremiah can choose an hourly rate of $9 plus a $50 weekly bonus for opening the store, or an hourly rate of $10 per hour with no opening bonus. The equations model his salary options.y = 9x + 50y = 10x What does x represent?

A
the number of times he opened the store
B
the number of hours worked per week
C
the total amount he earns each week
D
the amount of money earned per day
9

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
10

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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