Answers IN-Algebra IModeling with Systems of Linear Equations

Modeling with Systems of Linear Equations Answers

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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?

n + q = 28 0.05n + 0.25q = 4

n + q = 4 5n + 25q = 28

n + q = 28 5n + 25q = 4

n + q = 4 0.05n + 0.25q = 28

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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?

4c = h1.5c + 2h = 360

c = 4h1.5c + 2h = 360

c + h = 3601.5c = 4(2h)

c + h = 3604(1.5c) = 2h

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?

$2,500

$2,700

$2,800

$3,000

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?

50 − 2.5x = y 40 − 2x = y

50 + 2.5x = y 40 + 2x = y

50 − 2.5y = x 40 − 2y = x

50 + 2.5y = x 40 + 2y = x

Addison earns a fixed hourly rate working as a sales clerk. If she works on a holiday, she earns a different hourly rate than she earns on a regular day. In one week, she earns $188.50 by working 5 hours on a holiday and 16 hours during regular days. A different week, she earns $254.00 by working 8 hours on a holiday and 20 hours during regular days.How much more is Addison’s holiday hourly rate than her regular hourly rate?

$2.00

$8.50

$10.50

$19.00

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?

the number of times he opened the store

the number of hours worked per week

the total amount he earns each week

the amount of money earned per day

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.

9 = 0.5(x – y) 9 = 1.5(x + y)

9 = 1.5(x – y) 9 = 0.5(x + y)

0.5 = 9(x – y) 1.5 = 9(x + y)

1.5 = 9(x – y) 0.5 = 9(x + y)

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?

d = n + 10 d = 3n

d = n − 10 d = 3n

d = n + 10 n = 3d

d = n − 10 n = 3d

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?

3 miles per hour

8 miles per hour

11 miles per hour

14 miles per hour

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Modeling with Systems of Linear Equations Answers

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