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2013 AMC 10B Problem 2

2013 AMC 10B Problem 2AMC 10 Step by Step

Name: Date: September 13, 2026

Sets, Estimation & Miscellaneous · difficulty 1 of 5 · about 1 min · position P1-10

Mr. Green measures his rectangular garden by walking two of the sides and finding that it is $15$ steps by $20$ steps. Each of Mr. Green's steps is $2$ feet long. Mr. Green expects a half a pound of potatoes per square foot from his garden. How many pounds of potatoes does Mr. Green expect from his garden?

A)
$600$
B)
$800$
C)
$1000$
D)
$1200$
E)
$1400$

Answer

Key insight

Convert each side from steps to feet before finding the area; then the yield is half a pound per square foot.

Solution

Each step is $2$ feet, so the garden measures $15 \cdot 2 = 30$ feet by $20 \cdot 2 = 40$ feet.

Its area is $30 \cdot 40 = 1200$ square feet.

At half a pound per square foot, the expected yield is $\frac{1}{2} \cdot 1200 = 600$ pounds.

The answer is $\boxed{\textbf{(A)}\ 600}$ .

Why this works

Units drive the computation: lengths must be in feet before the area is in square feet, and only then does the "per square foot" rate apply. Converting both dimensions doubles each, so the area quadruples; a common error is to double the area only once.

The trap

Converting only one side to feet, or multiplying the area by 2 instead of by 1/2.

Common mistakes

Converting only one side to feet, or multiplying the area by 2 instead of by 1/2.
Computing the area in square steps ( $300$ ) and then multiplying by $2$ once, getting $600$ by luck or $300$ by mistake.

Techniques

Set up the equation/formula and compute; no special trick needed