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Fuel Consumption and Car Weight: An Inverse Variation Application
Problem: A car's fuel consumption (mpg) varies inversely with its weight. A car that weighs 3100 pounds gets 26 mpg on the highway. (a) Write the equation of variation. (b) What would be the fuel consumption of a car that weighs 4030 pounds?
Part (a) — Find the equation.
Let = fuel consumption and = weight. Because varies inversely with , write the inverse variation formula using these variables:
Substitute the known values and :
Solve for the constant of variation by multiplying both sides by 3100:
Substitute back into the formula:
Part (b) — Find when .
Substitute into the equation:
A car that weighs 4030 pounds would have a fuel consumption of 20 mpg. The heavier car gets fewer miles per gallon, which is consistent with the inverse relationship between weight and fuel efficiency.
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