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, 𝐢, in dollars, where π‘š is the monthly distance covered by the cars in miles. Small car: 𝐢 = (√3π‘š + 80)/2 and Medium car: 𝐢 = (π‘š/8) + 120. What is π‘š in terms of 𝐢 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, 𝐢, in dollars, where π‘š is the monthly distance covered by the cars in miles. For a small car, 𝐢 is equal to the square root of three π‘š plus 80 all divided by two. And for a medium car, 𝐢 is equal to π‘š divided by eight plus 120. What is π‘š in terms of 𝐢 in the equation for the maintenance cost of the medium car?

The equation given for the medium car was 𝐢 is equal to π‘š divided by eight plus 120. We need to rearrange this equation so that we have π‘š in terms of 𝐢. This means that we want to make π‘š 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 𝐢 minus 120. On the right-hand side, we’re just left with π‘š 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 𝐢 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, we’re left with eight multiplied by π‘š divided by eight. On this side, the eights will cancel, leaving us with one π‘š or just π‘š.

We’ve now rearranged the equation so that π‘š is the subject of the formula, where π‘š is equal to eight multiplied by 𝐢 minus 120. We can use this equation to calculate π‘š, the monthly distance covered by the car, when we are given 𝐢, the maintenance cost. The number of miles, π‘š, is equal to eight multiplied by 𝐢 minus 120, where 𝐢 is the cost in dollars of the monthly maintenance.

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