SOLUTION: Ivanna will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $45 and costs an additional $0.70 per mile driven. The second plan has

Question 1171112: Ivanna will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $45 and costs an additional $0.70 per mile driven. The second plan has no initial fee but costs $0.90 per mile driven.
For what amount of driving do the two plans cost the same?

What is the cost when the two plans cost the same?

Help please, thank you in advance.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

x = number of miles driven
y = total cost

First Plan:
If you drive 1 mile, then you are charged $0.70
If you drive x miles, then you are charged 0.70x dollars. This is on top of the $45 initial fee. In total, you pay y = 0.70x+45 for the first plan.

Second Plan:
There are no initial costs, but the cost per mile is higher. The equation here is y = 0.90x

We have this system of equations
y = 0.70x+45
y = 0.90x

Since y is equal to both 0.70x+45 and 0.90x, this means we can equate the right hand sides and solve for x

0.90x = 0.70x+45
0.90x-0.70x = 45
0.20x = 45
x = 45/0.20
x = 225

The two plans cost the same when you drive exactly 225 miles.

Plug this x value into either equation to find y
y = 0.70x+45 = 0.70*225+45 = 202.50
or
y = 0.90x = 0.90*225 = 202.50

You only need to pick on one equation, but doing both helps show that x = 225 leads to the same y value. This confirms our answers.

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Answers:
The plans cost the same when you drive 225 miles.
The cost is $202.50 when the plans cost the same.

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