Question

For a certain farm, soybean production increased by 25 percent from year X to year Y, and the selling price of soybeans decreased by 25 percent from year X to year Y. If the entire soybean production was sold each year, approximately what was the percent change in the revenues from the sale of the soybeans from year X to year Y?

• A. \( 56% \text{ decrease} \)
• B. \( 6% \text{ decrease} \)
• C. \( \text{No change} \)
• D. \( 6% \text{ increase} \)
• E. \( 56% \text{ increase} \)

Hint:

Multiply new production and price, compare to original.

Answer 1

The Correct Option is B

Step 1: Let initial production = 100 units, price = 100 per unit.
Step 2: Year X revenue = \( 100 \times 100 = 10,000 \).
Step 3: Year Y: production = \( 100 \times 1.25 = 125 \), price = \( 100 \times 0.75 = 75 \), revenue = \( 125 \times 75 = 9,375 \).
Step 4: Percent change = \( \frac{9,375 - 10,000}{10,000} \times 100 = -6.25% \approx 6% \text{ decrease} \).