A car rental company uses these equations to calculate estimates for the monthly maintenance costs of a car, 𝐶, in dollars, where 𝑚 is the monthly distance covered by the cars in miles. For a small car, 𝐶 is equal to the square root of three 𝑚 plus 80 all divided by two. And for a medium car, 𝐶 is equal to 𝑚 divided by eight plus 120. What is 𝑚 in terms of 𝐶 in the equation for the maintenance cost of the medium car?
The equation given for the medium car was 𝐶 is equal to 𝑚 divided by eight plus 120. We need to rearrange this equation so that we have 𝑚 in terms of 𝐶. This means that we want to make 𝑚 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 𝐶 minus 120. On the right-hand side, we’re just left with 𝑚 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 𝐶 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 𝑚 divided by eight. On this side, the eights will cancel, leaving us with one 𝑚 or just 𝑚.
We’ve now rearranged the equation so that 𝑚 is the subject of the formula, where 𝑚 is equal to eight multiplied by 𝐶 minus 120. We can use this equation to calculate 𝑚, the monthly distance covered by the car, when we are given 𝐶, the maintenance cost. The number of miles, 𝑚, is equal to eight multiplied by 𝐶 minus 120, where 𝐶 is the cost in dollars of the monthly maintenance.