Juan will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of
$49.98
and costs an additional
$0.16
per mile driven. The second plan has an initial fee of
$57.98
and costs an additional
$0.14
per mile driven. How many miles would Juan need to drive for the two plans to cost the same?

Question

Juan will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of 
$49.98
 and costs an additional 
$0.16
 per mile driven. The second plan has an initial fee of 
$57.98
 and costs an additional 
$0.14
 per mile driven. How many miles would Juan need to drive for the two plans to cost the same?

anonymous · Answer

juan to know the answer

igreen · Answer

We have two equations.

y = 0.16x + 49.98

and

y = 0.14x + 57.98

igreen · Answer

It's a system of equations.

y = 0.16x + 49.98
y = 0.14x + 57.98

Solve the system of equations using substitution.

0.16x + 49.98 = 0.14x + 57.98

Solve for 'x'

anonymous · Answer

x=400

anonymous · Answer

right? @iGreen

igreen · Answer

Yes, that's correct

0.02x + 49.98 = 57.98

0.02x = 8

x = 400

anonymous · Answer

yaay!!

igreen · Answer

So Juan needs to drive 400 miles for the two plans to be the same.