Question

A person needs to rent a​ 12-foot moving truck for a day. He calls two rental companies to determine their fee structure. The first company charges ​$25 plus 30 per​ mile, and the second company charges ​$30 plus 20 per mile?

Set up a system of linear equations in two variables that models the problem. Then solve the system of linear equations to determine the number of miles for which the costs of renting the truck will be the same. What is the cost at this​ mileage? If he plans to drive the truck for 150​ miles, which company should he​ use?

Answer 1

At `0.5` miles they both cost `40` dollars

You should choose Company 2 for driving 150 miles.

Explanation:

Let `x=`mileage and `y=`cost

An equation for company 1 can be represented by:
`y=25+30x`

Company 2:
`y=30+20x`

Set the two equations equal to each other:

`25+30x=y=30+20x`

Combine like terms:

`10x=5`
`x=0.5` Thus they have the same cost at half a mile.

Plug in `x=0.5` into either equation to determine the shared cost:

`y=25+30(0.5)`
`y=25+15=40` Thus the cost is 40 dollars at half a mile

Since Company 2’s cost is growing at a slower rate than Company 1 and `150>0.5` you should choose Company 2. To confirm this, just plug in `150` for `x` in both equations:

1: `y=25+30(150)=4525` dollars
2: `y=30+20(150)=3030` dollars

Therefore Company 2 is cheaper by `1495` dollars