Algebra word problem

Question

Miguel will rent a car for the weekend he can choose one of two plans. The first plan has an initial fee of $50 cost an additional $.30 per mile driven the second plan has no additional fee because $.80 per mile driven for what amount of driving to the two plans cost the same? What is the cost whento plan to plans cost the same?

Answer 1

Let m₁ be the number of miles driven on the first plan, and c₁ be the total cost of the first plan.

Then

c₁ = 0.3×m₁ + 50

Let m₂ be the number of miles driven on the second plan, and c₂ be the total cost of the second plan.

Then

c2 = 0.8×m₂

To find out the amount of driving ( in other words, when the mileage on both plans) results in equal total costs, set the costs equal and use the cost expressions to solve for the mileage.

Since m₁ will equal m₂ when c₁ = c₂, let's now just use m for the mileage.

0.8m = 0.3m + 50

Subtract .3m from both sides:

0.5m = 50

Divide both sides by 0.5

m = 100

Checking,

0.8 × 100 = 80

and

0.3×100 + 50 = 30 + 50 = 80

So, our answer of 100 miles does check out, and as a bonus, we also know that the cost would be $80.

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