Questions: Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value. When sales representatives for a pharmaceutical company drive to out-of-town meetings that require an overnight stay, they receive 160 for lodging plus 0.65 per mile driven. How many miles did Joe drive if his company reimbursed him 322.50 for an overnight trip? The equation is .

Solution Steps

To solve this problem, we need to set up an equation based on the given information. Joe receives a fixed amount for lodging and an additional amount per mile driven. We can express the total reimbursement as the sum of these two components and solve for the number of miles driven.

1. Let \( x \) be the number of miles Joe drove.
2. The total reimbursement is given by the equation: \( 160 + 0.65x = 322.50 \).
3. Solve this equation for \( x \) to find the number of miles driven.

To determine the number of miles Joe drove, we start with the equation for total reimbursement: \[ 160 + 0.65x = 322.50 \]

Subtract the lodging cost from the total reimbursement: \[ 0.65x = 322.50 - 160 \]

Calculate the right-hand side: \[ 0.65x = 162.50 \]

Divide both sides by the reimbursement per mile to solve for \( x \): \[ x = \frac{162.50}{0.65} \]

Perform the division: \[ x = 250.0 \]

Final Answer