$\"\"$

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The U.S. Mint produces quarters that weigh about $\"\"$ each.

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After the quarters are produced, a machine weighs them.

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If the quarter weighs $\"\"$ more or less than the desired weight, the quarter is rejected.

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Find the heaviest and lightest quarters the machine will approve.

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The equation is $\"\"$ .

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Case(i):

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$\"\"$ (First equation)

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$\"\"$ (Add $\"\"$ to each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Add: $\"\"$ )

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Case(ii):

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$\"\"$ (Second equation)

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$\"\"$ (Add $\"\"$ to each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Subtract: $\"\"$ )

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Therefore, the machine approved heaviest is $\"\"$ and lightest $\"\"$ .

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$\"\"$

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The machine would approved heaviest is $\"\"$ and lightest $\"\"$ .