Juan will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of
$57.98
and costs an additional
$0.09
per mile driven. The second plan has an initial fee of
$49.98
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?
To find the number of miles that Juan would need to drive for the two plans to cost the same, we can set up an equation.
Let's assume x represents the number of miles driven.
For the first plan, the total cost can be expressed as:
$57.98 + $0.09x
For the second plan, the total cost can be expressed as:
$49.98 + $0.14x
We want to find the value of x for which the two plans have the same cost. So we set up the equation:
$57.98 + $0.09x = $49.98 + $0.14x
Now, let's solve this equation to find the value of x.
Subtract $49.98 from both sides:
$57.98 - $49.98 + $0.09x = $0.14x
Combine like terms:
$8 + $0.09x = $0.14x
Subtract $0.09x from both sides:
$8 = $0.14x - $0.09x
Combine like terms:
$8 = $0.05x
Divide both sides by $0.05:
$8 / $0.05 = x
x = 160
Therefore, Juan would need to drive 160 miles for the two plans to cost the same.
solve for m, the number of miles
.09m + 57.98 = .14m + 49.98
9m + 5798 = 14m + 4998
...