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Question

Difficulty: MediumDirect Proportions

During a facility expansion, a landscaping crew uses 2.52.5 pounds of specialized grass seed to cover a 400400-square-foot section of terrain. Operating at this exact constant rate, how many ounces of grass seed will be required to cover a 3,2003,200-square-foot sector?

  1. 320320Answer
  2. B
    2020
  3. C
    3,2003,200
  4. D
    1.251.25

Answer

The correct answer is 320320.
The correct answer is found by setting up a direct proportion. Since 3,2003,200 square feet is exactly 88 times larger than 400400 square feet, the amount of seed required must also be 88 times the original amount. Multiplying 2.52.5 pounds by 88 gives 2020 pounds of seed. Finally, converting 2020 pounds into ounces by multiplying by 1616 (since 11 pound = 1616 ounces) yields exactly 320320 ounces.

Step-by-Step Solution

1
Determine the scale factor by dividing the target area by the initial area.
3,200÷400=83,200 \div 400 = 8
This establishes how many times larger the new sector is compared to the original section.
2
Multiply the initial amount of grass seed by the scale factor to find the total pounds needed.
2.5×8=202.5 \times 8 = 20 pounds
Because this is a direct proportion, the amount of seed scales by the exact same factor as the area.
3
Convert the total weight from pounds to ounces.
20×16=32020 \times 16 = 320 ounces
The question specifically asks for the final answer in ounces, and there are 16 ounces in 1 pound.

Key Concept

Direct Proportions and Unit Conversion

Alternative Method

Convert the initial seed amount to ounces first: 2.52.5 pounds = 4040 ounces. Then, set up the proportion: 40400=x3,200\frac{40}{400} = \frac{x}{3,200}. Solving for xx gives x=40×8=320x = 40 \times 8 = 320.
Estimated Time:1m 15s
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Topics

Direct Proportions

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