Question

groundskeepers work to look after football fields, golf courses, parks, and so on. one thing they do is fertilize a field. the label tells the groundskeeper that 36 pounds will treat 10,000 square feet. the formula below can be used to tell how much fertilizer the groundskeeper should use: \\(\frac{36}{10,000} = \frac{f}{a}\\), where \\(f\\) is the amount of fertilizer in pounds used, and \\(a\\) is the area of the field in square feet. how much fertilizer would be needed to fertilize a 54,000 square foot soccer field?

a. 6.67 pounds
b. 194.4 pounds
c. 264.3 pounds
d. 62.3 pounds

Explanation:

Identify the given values and formula

We are given the proportion formula:

$$ \frac{36}{10,000} = \frac{f}{a} $$

where:

• \(f\) is the amount of fertilizer in pounds.
• \(a\) is the area of the field in square feet.
• The target area is \(a = 54,000\) square feet.

Substitute the given area into the formula

Using the Algebraic Evaluation knowledge point

$$ \frac{36}{10,000} = \frac{f}{54,000} $$

Solve the equation for the unknown variable

Using the Linear Equation Solving knowledge point

$$
LATEXBLOCK0
$$

Answer:

• (A) 6.67 pounds
• (B) 194.4 pounds (Correct answer)
• (C) 264.3 pounds
• (D) 62.3 pounds