Question

Set up and solve a proportion for the following application problem. If 5 pounds of grass seed cover 367 square​ feet, how many pounds are needed for 5872 square​ feet?
Question content area bottom
Part 1
  
enter your response here pounds.

Answer 1

To set up the proportion, we can relate the number of pounds of grass seed to the area it covers. Given that 5 pounds covers 367 square feet, we can represent the unknown number of pounds needed for 5872 square feet using a proportion.

Set up the proportion as follows:

\[
\frac{5 \text{ pounds}}{367 \text{ square feet}} = \frac{x \text{ pounds}}{5872 \text{ square feet}}
\]

Now, we can cross-multiply to solve for \( x \):

\[
5 \times 5872 = 367 \times x
\]

Calculating the left side:

\[
5 \times 5872 = 29360
\]

Now we rewrite the equation:

\[
29360 = 367x
\]

To solve for \( x \), divide both sides by 367:

\[
x = \frac{29360}{367}
\]

Now, performing the division:

\[
x \approx 80
\]

Thus, the number of pounds needed for 5872 square feet is approximately:

\[
\boxed{80} \text{ pounds}
\]