Question

set up and solve a proportion for the following application problem. if 2 pounds of grass seed cover 414 square feet, how many pounds are needed for 7038 square feet?
pounds

Explanation:

Step1: Define variables and set up proportion

Let \( x \) be the pounds of grass seed needed for 7038 square feet. The proportion is \(\frac{2}{414}=\frac{x}{7038}\) (since the rate of grass seed per square foot is constant).

Step2: Cross - multiply to solve for \( x \)

Cross - multiplying gives \( 414x = 2\times7038 \). First, calculate \( 2\times7038 = 14076 \). Then, solve for \( x \) by dividing both sides of the equation by 414: \( x=\frac{14076}{414} \).

Step3: Simplify the division

\(\frac{14076}{414}=34\) (because \( 414\times34 = 14076 \)).

Answer:

34