2021 Fall AMC 10A Problems/Problem 2

Problem

Menkara has a $4 \times 6$ index card. If she shortens the length of one side of this card by $1$ inch, the card would have area $18$ square inches. What would the area of the card be in square inches if instead she shortens the length of the other side by $1$ inch?

$\textbf{(A) } 16 \qquad\textbf{(B) } 17 \qquad\textbf{(C) } 18 \qquad\textbf{(D) } 19 \qquad\textbf{(E) } 20$

Solution

If Menkara instead shortens the length of the other side by $1$ inch, then the dimensions of the index card will be $4\times5,$ with area $\boxed{\textbf{(E) } 20}.$

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2021 Fall AMC 10A Problems/Problem 2

Problem

Solution