Question

A 2 pound bag of grass seed covers 5,000 square feet. How many pounds would be needed to cover 18,000 square feet?Write answer as an integer or a reduced fraction.

Answer 1

Explanation

This exercise is about direct proportionality. We have two quantities: # of pound bags of grass seed, and square feet of land. They are directly proportional, and we know that 2 pound bags "correspond" (covers) with 5000 square feet. Then, if x denotes the pound bags that covers 18000 square feet, the following equation must hold:

$\frac{x}{18000}=\frac{2}{5000}\text{.}$

Comment: In simple words, direct proportionality says that dividing a number of pound bags of grass by the square feet they cover gives always the same number!

Solving the above equation for x, we get

$\begin{gathered} \frac{x}{18000}=\frac{2}{5000}, \\ x=18000\cdot\frac{2}{5000}, \\ x=\frac{36000}{5000}, \\ x=\frac{36}{5}\text{.} \end{gathered}$Answer

To cover 18000 square feet it's needed 36/5 pound bags of grass seed.