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

Step-by-step 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:

`(x)/(18000)=(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} (x)/(18000)=(2)/(5000), \\ x=18000\cdot(2)/(5000), \\ x=(36000)/(5000), \\ x=(36)/(5)\text{.} \end{gathered}`Answer

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