math word problems

Question

A truck can be rented from Company A for ​$90 a day plus ​$0.50 per mile. Company B charges ​$60 a day plus ​$0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

Answer 1

Hi Ashlyn..

A truck can be rented from Company A for ​$90 a day plus ​$0.50 per mile. Company B charges ​$60 a day plus ​$0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

For word problems, identify the given information. Identify what the problem is asking for.

Given:

Company A for ​$90 a day plus ​$0.50 per mile

Company B charges ​$60 a day plus ​$0.80 per mile

Find: The number of miles in a day where rental cost is the same

Implied information:

We are told that this would be the cost in a day, so there is only 1 day of daily rental.

We are to find the number of miles where the rental cost is the same. So we would drive the same number of miles and have the same cost for each rental.

The total cost of Rental would be the cost for 1 day plus the cost per mile times the number of miles

Let m = number of miles driven. (This will be the same for both rentals)

Cost A = $90 + ($0.50 x m)

Cost B = $60 + ($0.80 x m)

Now since we are trying to find when the costs would be equal, we can set both equations equal to eachother.

$90 + ($0.50 x m) = $60 + ($0.80 x m) Now you need to solve for m

90 + 0.5 m = 60 + 0.8 m

30 = 0.3 m

100 = m

So at 100 miles, the cost for both rentals would be the same..

Let's check to make sure we did the problem correctly

Cost A = $90 + ($0.50 x m)

Cost A = 90 + 0.5 x 100

Cost A = 90 + 50 = $140

Cost B = $60 + ($0.80 x m)

Cost B = 60 + 0.8 x 100

Cost B = 60 + 80 = $140.

Both costs are the same. So our answer was correct.

At 100 miles the cost of both rentals would be the same.

Let me know if you need more help!