Question

Josiah owns a trucking company. For every truck that goes out, Josiah must pay the

driver $24 per hour of driving and also has an expense of $2.75 per mile driven for
gas and maintenance. On one particular day, the driver drove an average of 30 miles
per hour and Josiah's total expenses for the driver, gas and truck maintenance were
$1171.50. 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 system of equation would be 30×2.75+(1171.50÷24)

Answer 2

24*x + 2.75*y = 1171.5 (eq. 1)

y/x = 30 (eq. 2)

Solution: x = 11; y = 330

Explanation:

Let's define:

x: hours driven

y: miles driven

The mathematical expression of the Josiah's total expenses for the driver is:

Expenses = 24*x + 2.75*y

On the particular day cited, the following 2 equations must be satisfied:

24*x + 2.75*y = 1171.5 (eq. 1)

y/x = 30 (eq. 2)

Dividing equation 1 by x and replacing with equation 2, we get:

24 + 2.75 * y/x = 1171.5/x

24 + 2.75*30 = 1171.5/x

x = 1171.5/106.5 = 11

Then:

y = 30*11 = 330