Question

Xin owns a trucking company. for every truck that goes out, xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile driven for gas and maintenance. on one particular day, the driver drove an average of 50 miles per hour and xin's total expenses for the driver, gas and truck maintenance were $1457.50. write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. define the variables that you use to write the system.

Answer 1

The number of miles that the truck drove is 550 miles.

How to illustrate the information?

From the information, Xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile. This can be illustrated as:

20x + 2.25y = 1457.50 ....... i

x = number of hours

y = number of miles driven

The driver drove an average of 50 miles per hour. This will be illustrated as:

y/x = 50

y = 50x

Substitute into equation i

20x + 2.25y = 1457.50

20x + 2.25(50x) = 1457.50

20x + 112.50x = 1457.50

Collect like terms

132.50x = 1457.50

Divide

x = 1457.50 / 132.50

x = 11

y = 50x = 50 × 11 = 550 miles

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