2013 AMC 10B Problem 2

The potato rate is given per square foot, so we need the area in square feet. The side lengths are in steps, so change them to feet first.

1. Each step is $2$ feet long:
- $15$ steps $= 15 \times 2 = 30$ feet,
- $20$ steps $= 20 \times 2 = 40$ feet.
2. The garden is a rectangle, so its area is $30 \times 40 = 1200$ square feet.
3. Each square foot gives half a pound, so the garden gives $1200 \times \frac{1}{2} = 600$ pounds.

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

Before you use a rate like "per square foot", make sure your quantity is measured in that unit. Notice that both sides doubled, so the area became $2 \times 2 = 4$ times bigger: $15 \times 20 = 300$ square steps is $4 \times 300 = 1200$ square feet. Doubling the area only once is a common slip.

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 $\boxed{\textbf{(A)}\ 600}$.