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

Answer:

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

Part B: $200$ miles

Step-by-step 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.