Question

Rita's company reimburses her expenses on food, lodging, and conveyance during business trips. The company pays $55 a day for food and lodging and $0.45 for each mile traveled. Rita drove 300 miles and was reimbursed $2,335.

Part A: Create an equation that will determine the number of days x on the trip. 
Part B: Solve this equation justifying each step with an algebraic property of equality. Part C: How many days did Rita spend on this trip?

Answer 1

"The company pays $55 a day for food and lodging and $0.45 for each mile traveled" means that if she travels m miles and is on a trip for x days then Rita will receive:

55x + 0.45m dollars.


Rita drove 300 miles, means that m=300. Thus 55x + 0.45m becomes


`55x+0.45m=55x+0.45 \cdot 300=55x+135` (dollars.)

She was reimbursed $2,335 means that
`55x+135=2,335`.


Part A:
`55x+135=2,335`.

Part B:

We are given the equation 55x+135=2,335. Subtracting 135 from both sides we have:

55x=2,335-135=2,200.

Dividing both sides by 55, we get: x=2,200/55=40.


Part C: since x represents the number of days Rita spend on this trip, and x=40, then Rita spent 40 days on this trip.