Multi-Step Word Problems

A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. How many miles would have to be driven in one day for both rental agencies to cost the same amount to rent?

• 120 miles

• 100 miles

• 110 miles

• 150 miles 

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8.17

Which is the mistake the student made?

• The student did not distribute properly.

• The student did not combine like terms properly.

• The student did not divide by the proper value.

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8.17

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

• 15x + 2.5 = 10x + 3

• 15 - 2.5x = 10 - 3x

• 15 + 2.5x = 10 + 3x

• 15 - 10 = 2.5x + 3x

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8.17

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal?

• 150x + 24 = 180 + 20x

• 150 + 24x = 180 + 20x

• 180 - 150 = 24 x + 20x

• 150 - 24x = 180 - 20x

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8.17

Brambleton Park has 26 walking trails. Lawrence State Park has 8 times more walking trails than Brambleton Park. Prince William National Park has 97 more walking trails than Lawrence State Park. How many walking trails does Prince William National Park have?

• 20,176 trails

• 305 trails

• 131 trails

• 123 trails

An art teacher had 237 colored pencils left over from last year. This year, he bought 26 boxes of colored pencils that had 16 pencils in each. He also bought 15 boxes that had 54 pencils in each. Finally, when he was sorting the pencils, 19 rolled under the cabinet and were lost.

Solve the following equation to determine c, the number of colored pencils the art teacher has now.

c = 237 + [ (26 ∙ 16) + (15 ∙ 54) ] – 19

• 2,179

• 187,652

• 1,444

• 183,095

An art teacher had 237 colored pencils left over from last year. This year, he bought 26 boxes of colored pencils that had 16 pencils in each. He also bought 15 boxes that had 54 pencils in each. Finally, when he was sorting the pencils, 19 rolled under the cabinet and were lost. Solve the following equation to determine c, the number of colored pencils the art teacher has now. c = 237 + [ (26 ∙ 16) + (15 ∙ 54) ] – 19

• 2,179

• 187,652

• 1,444

• 183,095

Taxi company A charges $8.00 to get into the cab and $0.75 per mile. Taxi company B charges $6.00 to get into a cab and $1.25 per mile. How many miles would the cost be the same for both companies?

• 2 miles 

• 4 miles

• 0.50 mile

• -4 miles 

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8.17

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

• 3 hours

• 4 hours

• 1 hour

• 2 hours

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8.17

The length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle.

• 68

• 47

• 84

• 20

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8.17