Question

1. in langley, british columbia, you can rent a backhoe for $399 per day and a bulldozer for $550 per day. it costs $160, round trip to move each piece of equipment back and forth to the job site.

a) write an expression for the total cost of renting the backhoe, before tax. include transportation to and from the job site. what does your variable represent?
b) what is an expression for the total cost of renting and moving the bulldozer? use the same variable as in part a).
c) what is an expression for the cost of renting both a backhoe and a bulldozer? give your answer in its simplest form.
d) what is an expression for the difference in cost between renting the backhoe and the bulldozer? give your answer in simplest form.

Explanation:

Step1: Define Variables

Let \( d \) be the number of days renting the backhoe. The daily cost for the backhoe is $399, and the transportation cost is a one - time $160. So the total cost \( C_{backhoe} \) is the sum of the daily cost times the number of days and the transportation cost.
\( C_{backhoe}=399d + 160 \)

Step2: Analyze the Variable

The variable \( d \) in the expression \( 399d+160 \) represents the number of days the backhoe is rented. Because the $399 cost is per day, multiplying it by LXI2 (the number of days) gives the total daily - rental cost, and then we add the one - time transportation cost of $160.

Answer:

The variable \( d \) represents the number of days the backhoe is rented. The expression for the total cost of renting the backhoe is \( 399d + 160 \), where \( d \) is the number of days of rental.