A truck can be rented from company A for $90 a day plus $.40 per mile. Company B charges $30 a day plus $.70 per mile.

Question

For company A to have a better deal, the truck must be driven more than ____ miles per day.

Answer 1

Let the truck is driven X miles per day

Charges of company A will be = 90+0.4X

Charges of company B will be =30+0.7X

Let us find out value of X when charges of both companies are same

which means that   90+0.4 X= 30+0.7X

                             90-30      = 0.7X-0.4X

                             60    = 0.3X

                              60/0.3 = X 

                              X= 200

The charges of both companies will be same if truck is driven 200 miles per day

Company A will have better deal if truck is driven more than 200 miles per day ( because per mile rate of company A is less than company B)

Answer 2

There are two steps to this problem. The first step is to make an equation for the cost of each company. The cost of each one involves 2 variables. However, we can ignore the number of days since the question asks for per day.

CostA = 90 + .40(miles)

CostB = 30 + .70(miles)

We want to know when A is a better deal or when A costs less. That is when CostA < CostB. We can then substitute the right sides of our equations into the inequality. This will give:

90 + .40(miles) < 30 + .70(miles)     This is where we will now begin to solve for the number of miles.

-30                      -30                       Subtract 30 from both sides.

60 + .4(miles) < .7(miles)                Simplify

       -.4(miles)   -.4(miles)                Subtract .4(miles) from both sides

60 < .3(miles)                                 Simplify

/.3     /.3                                        Divide both sides by .3

200 < miles                                   Simplify

So for A to cost less the number of miles must be greater than 200.