Question

A truck can be rented from company A for $120 a day plus $0.50 per mile. Company b chargers $80 a day plus $0.70 per mile to rent the same truck. Part A write a equation. To find the number of miles in a day at which the rental costs for company A and company B are the same Part b solve the equation

Answer 1

Part A:
`.50x+120 = .70x+80`

Part B:
`200` miles

Explanation:

So to start, we need to put this information into slope-intercept form. Slope intercept form is
`y=mx+b` where
`m` represents the slope of a line and
`b` represents the y-intercept. In this question
`y` represents the total cost of the rental,
`x` represents the number of miles driven,
`m` represents the price per mile, and
`b` represents the base price of the rental. Now that we know the variables, we need to plug in the information we have.

Since we know that company A charges $125 a day and $0.50 per mile we would have
`y=.50x+120`

Since we know that company B charges $80 a day and $0.70 per mile we would have
`y=.70x+80`

Now that we have two equations we can move onto the next step. We're looking to know the number of miles (
`x`) that would make the total cost (
`y`) equal. To do this we can make the equations equal each other since we know that
`y` will be the same.

Written out, the equation will look like this:
`.50x+120 = .70x+80`

Now, we are trying to find
`x` so we need to isolate the variable.

To start we need to put
`x` on the same side so we'll subtract
`.70x` from both sides to get
`-.20x+120=80`

Next, we'll subtract
`120` from both sides of the equation to get
`-.20x=-40`

Finally, we'll divide both sides by
`-.20` to get
`x=200`

This means that at
`200` miles, both companies will cost the same amount.