$Motorcycle Valve Clearance Calculation and Spacer Size Word Problem$

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$Motorcycle Valve Clearance Calculation and Spacer Size Word Problem$

You are a mechanic who is measuring the valve clearance on a motorcycle engine. The current clearance for one of the valves is 0.30 millimeters (mm). The clearance should be at least 0.18 mm and no more than 0.22 mm. The valve clearance is set by using a spacer that reduces the distance between the cam and the valve by the size of the spacer. Spacers are available in 0.04 mm increments, and the spacer currently in the motorcycle engine is 2.84 mm. Which of the following size spacers, in millimeters, should you use to achieve a correct valve clearance?

Answer Options:
-2.54
-2.62
-2.76
-2.80
-2.92

Algebra

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Let $x$ be the size of the spacer. The current clearance is $0.30$. The size of the current spacer is $2.84$ which is going to be removed. So after removing the current spacer and installing the new one, the clearance will be
\[0.30+x-2.84=x-2.54\]
which should be at least $0.18$ mm and no more than $0.22$, i.e.
\[0.18 \leq x-2.54 \leq 0.22\]
\[\Rightarrow 0.18+2.54 \leq x\leq 0.22+2.54 \]
\[\Rightarrow 2.72 \leq x\leq 2.76. \]
The only answer that satisfies the above inequality is $2.76$. So the correct answer is $2.76$

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$Motorcycle Valve Clearance Calculation and Spacer Size Word Problem$

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