AnswersCommon Core Algebra I A-ICSolving One-Variable Inequalities

Modeling with Systems of Linear Equations Answers

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1
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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
2
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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)
3

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
4

A salesperson earns a commission based on the number and type of vehicle sold. A person selling 6 cars and 3 trucks earns $4,800. A person selling 8 cars and 1 truck earns $4,600. How much does a salesperson earn for selling 2 cars and 3 trucks?

A
$2,500
B
$2,700
C
$2,800
D
$3,000
5

Students are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. There are 15 questions on the test, and students are given 51 minutes to take it.The system of equations shown can be used to find the number of multiple-choice questions, m, and the number of free-response questions, f, on the test.m + f = 153m + 5f = 51How many multiple-choice questions are on the test?

A
3
B
5
C
12
D
14
6

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
7

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
8

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
9

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
10

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
11

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
12

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
13

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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