Expression Word Problems

Question

Company A charges $55 per day and .35 per mile. Company B charges $50 per day and .40 per mile. After how many miles will the companies be charging the same amount?

Answer 1

55 + 0.35*N = 50 + 0.40*N

 

0 = 50 + 0.40*N - 55 - 0.35*N <--- everyone to the right side

 

0 = 0.05*N - 5

 

5/0.05 = N

 

500/5 = N

 

N = 100

 

At 100 miles, company A charges 55 + 100*0.35 = 55 + 35 = $90

            while company B charges 50 + 100*0.40 = 50 + 40 = $90

 

So if you are going less than 100 miles, choose company B; otherwise company A is cheaper

 

Alternatively, you can view the solution to the problem like this:

  The difference of the flat rates is 55-50 = $5

 The differences in the mileage fees is 0.05 or 1 nickle per mile.

 

So how many miles are needed to compensate, erase, and cancel the $5 difference?

  5 / 0.05 = 500/5 = 100