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Solving Systems of Linear Inequalities Answers

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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?

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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

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

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

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 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)

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.

0.75(x + y) = 120 x − y = 120

0.75(x − y)= 120 x + y = 120

120(x + y) = 0.75 120(x − y) = 1

120(x − y) = 0.75 120(x + y) = 1

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

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

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