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. (3 points)

Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points)

Part C: How many days did Rita spend on this trip? (1 point)

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. (3 points)

Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points)

Part C: How many days did Rita spend on this trip? (1 point)

Mercury · Answer

part A)

let's just consider the amount reimbursed for food + lodging. let x = number of days. if they reimburse $55 for each day's food and lodging, then the total amount reimbursed for food and lodging is naturally 55*x

similar logic for the the miles travelled (reimbursement per mile) * (number of miles). plug in rita's reimbursement per mile and # of miles travelled.

add the two reimbursement types together then sum up to the total amount reimbursed. this will be your equation for part A)

Mercury · Answer

for part B) solve the equation from part A). remember, to isolate x, do the opposite of what is being done to x, starting with "undoing" any addition or subtraction.  make sure you justify each step with the appropriate algebraic property. ex: if you subtract a certain # of both sides, you're using the subtraction property of equality.

for part C) report your x-value after you solve the equation