AnswersOC27 MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006PModeling with Systems of Linear Equations

Modeling with Systems of Linear Equations Answers

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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
2
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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
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

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
5

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
6

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
7

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
8

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
9

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
10

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

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