Salma will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $47.98 and costs an additional $0.16 per mile driven. The second plan has an initial fee of $51.98 and costs an additional $0.12 per mile driven. How many miles would Salma need to drive for the two plans to cost the same?
m = numbers of driven miles
The two plans to cost the same when:
47.98 + 0.16 m = 51.98 + 0.12 m
0.16 m - 0.12 m = 51.98 - 47.98
0.04 m = 4
m = 4 / 0.04 = 100 miles
Checking the results:
47.98 + 0.16 ∙ 100 = 51.98 + 0.12 ∙ 100
47.98 + 16 = 51.98 + 12
63.98 = 63.98
To find the number of miles Salma would need to drive for the two plans to cost the same, we'll set up an equation.
Let's assume the number of miles driven is 'm'.
For the first plan, the total cost would be the sum of the initial fee and the cost per mile:
Total cost of first plan = $47.98 + ($0.16 * m)
For the second plan, the total cost would be the sum of the initial fee and the cost per mile:
Total cost of second plan = $51.98 + ($0.12 * m)
To find the point at which both plans cost the same, we'll set up the equation:
$47.98 + ($0.16 * m) = $51.98 + ($0.12 * m)
Now, let's solve the equation for 'm':
$0.16 * m - $0.12 * m = $51.98 - $47.98
$0.04 * m = $4
m = $4 / $0.04
m = 100
So, Salma would need to drive 100 miles for the two plans to cost the same.