Question

Alonzo will rent a car for the weekend. He can choose one of two plans. The first plan has an intial fee of $44 and an additional cost of $0.12 per mile driven. The second plan has an intial fee of $51 and costs an additional $0.08 per mile driven. For what amount of driving do the two plans cost the same? What is the cost wheb the two plans cost the same?

Answer 1

Answer:

The both plans will cost same for driving 175 miles.

The cost will be $65, when two plans cost the same.

Step-by-step explanation:

Let x represent number of miles.

We have been given that the first plan has an initial fee of $44 and an additional cost of $0.12 per mile driven. So total cost for x miles using 1st plan would be $44+0.12x$.

The second plan has an initial fee of $51 and costs an additional $0.08 per mile driven. So total cost for x miles using 2nd plan would be $51+0.08x$.

To find the number of miles for which both plans will cost same, we will equate both expressions and solve for x as:

$44+0.12x=51+0.08x$

$44+0.12x-0.08x=51+0.08x-0.08x$

$44+0.04x=51$

$44-44+0.04x=51-44$

$0.04x=7$

$\frac{0.04x}{0.04}=\frac{7}{0.04}$

$x=175$

Therefore, the both plans will cost same for driving 175 miles.

To find the cost we will substitute $x=175$ in expression $44+0.12x$ as:

$44+0.12(175)=44+21=65$

Therefore, the cost will be $65, when two plans cost the same.