# Video: SAT Practice Test 1 β’ Section 4 β’ Question 22

A car rental company uses these equations to calculate estimates for the monthly maintenance costs of a car, πΆ, in dollars, where π is the monthly distance covered by the cars in miles. Small car: πΆ = (β3π + 80)/2 and Medium car: πΆ = (π/8) + 120. What is π in terms of πΆ in the equation for the maintenance cost of the medium car?

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### Video Transcript

A car rental company uses these equations to calculate estimates for the monthly maintenance costs of a car, πΆ, in dollars, where π is the monthly distance covered by the cars in miles. For a small car, πΆ is equal to the square root of three π plus 80 all divided by two. And for a medium car, πΆ is equal to π divided by eight plus 120. What is π in terms of πΆ in the equation for the maintenance cost of the medium car?

The equation given for the medium car was πΆ is equal to π divided by eight plus 120. We need to rearrange this equation so that we have π in terms of πΆ. This means that we want to make π the subject of the formula.

In order to balance or rearrange a formula, we need to do the same to both sides of the equation. In this case, our first step will be to subtract 120 from both sides. On the left-hand side, this leaves us with πΆ minus 120. On the right-hand side, weβre just left with π divided by eight, as 120 minus 120 is equal to zero.

Our second step is to multiply both sides of the equation by eight. On the left-hand side, we are left with eight multiplied by πΆ minus 120. We could expand or multiply out this parenthesis. But for the purpose of this question, we will leave it as it is. On the right-hand side, weβre left with eight multiplied by π divided by eight. On this side, the eights will cancel, leaving us with one π or just π.

Weβve now rearranged the equation so that π is the subject of the formula, where π is equal to eight multiplied by πΆ minus 120. We can use this equation to calculate π, the monthly distance covered by the car, when we are given πΆ, the maintenance cost. The number of miles, π, is equal to eight multiplied by πΆ minus 120, where πΆ is the cost in dollars of the monthly maintenance.