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?

Question

08-01-2018
Mathematics

contestada

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?

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eco92 eco92 · Answer 1 · 2018-01-08T19:31:27+01:00

"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

[tex]55x+0.45m=55x+0.45 \cdot 300=55x+135[/tex] (dollars.)

She was reimbursed $2,335 means that [tex]55x+135=2,335[/tex].

Part A: [tex]55x+135=2,335[/tex].

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.