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A car rental company uses these equations to calculate estimates for the monthly maintenance costs of a car, πΆ, in dollars, where π is the monthly distance covered by the cars in miles.
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For a small car, πΆ is equal to the square root of three π plus 80 all divided by two.
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And for a medium car, πΆ is equal to π divided by eight plus 120.
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What is π in terms of πΆ in the equation for the maintenance cost of the medium car?
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The equation given for the medium car was πΆ is equal to π divided by eight plus 120.
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We need to rearrange this equation so that we have π in terms of πΆ.
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This means that we want to make π the subject of the formula.
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In order to balance or rearrange a formula, we need to do the same to both sides of the equation.
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In this case, our first step will be to subtract 120 from both sides.
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On the left-hand side, this leaves us with πΆ minus 120.
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On the right-hand side, weβre just left with π divided by eight, as 120 minus 120 is equal to zero.
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Our second step is to multiply both sides of the equation by eight.
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On the left-hand side, we are left with eight multiplied by πΆ minus 120.
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We could expand or multiply out this parenthesis.
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But for the purpose of this question, we will leave it as it is.
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On the right-hand side, weβre left with eight multiplied by π divided by eight.
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On this side, the eights will cancel, leaving us with one π or just π.
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Weβve now rearranged the equation so that π is the subject of the formula, where π is equal to eight multiplied by πΆ minus 120.
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We can use this equation to calculate π, the monthly distance covered by the car, when we are given πΆ, the maintenance cost.
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The number of miles, π, is equal to eight multiplied by πΆ minus 120, where πΆ is the cost in dollars of the monthly maintenance.