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| − | == Problem ==
| + | #REDIRECT [[2021_Fall_AMC_12A_Problems/Problem_2]] |
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| − | Menkara has a <math>4 \times 6</math> index card. If she shortens the length of one side of this card by <math>1</math> inch, the card would have area <math>18</math> square inches. What would the area of the card be in square inches if instead she shortens the length of the other side by <math>1</math> inch?
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| − | <math>\textbf{(A) } 16 \qquad\textbf{(B) } 17 \qquad\textbf{(C) } 18 \qquad\textbf{(D) } 19 \qquad\textbf{(E) } 20</math>
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| − | == Solution ==
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| − | We construct the following table:
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| − | <cmath>\begin{array}{c||c|c||c}
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| − | & & & \\ [-2.5ex]
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| − | \textbf{Scenario} & \textbf{Length} & \textbf{Width} & \textbf{Area} \\ [0.5ex]
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| − | \hline
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| − | & & & \\ [-2ex]
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| − | \textbf{Initial} & 4 & 6 & 24 \\
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| − | \textbf{Menkara shortens one side.} & 3 & 6 & 18 \\
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| − | \textbf{Menkara shortens other side instead.} & 4 & 5 & 20
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| − | \end{array}</cmath>
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| − | Therefore, the answer is <math>\boxed{\textbf{(E) } 20}.</math>
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| − | ~MRENTHUSIASM
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| − | ==See Also==
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| − | {{AMC10 box|year=2021 Fall|ab=A|num-b=1|num-a=3}}
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| − | {{MAA Notice}}
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