Question

Paj is filling a 9-inch- flower pot with soil from small bags. Each bag of soil contains 2 2/3 cubic inches of soil. Exactly how many bags of soil are needed for paj to fill the flower pot

Answer 1

`Number\ of\ bags = 3{(3)/(8)`

Explanation:

Given

Size of Flower Pot = 9 cubic-inch

Size of filling bag =
`2(2)/(3)` cubic-inch

Required

Determine the number of bags needed to fill the pot

To solve this, we simply divide the volume of the flower pot by the volume of the filling bags;

This is shown as follows:

`Number\ of\ bags = (Volume\ of\ Pot)/(Volume\ of\ filling\ bags)`

Substitute 9 for Volume of Pot and
`2(2)/(3)` for Volume of filling bags

`Number\ of\ bags = (9)/(2(2)/(3))`

Convert denominator to improper fraction

`Number\ of\ bags = (9)/((8)/(3))`

Rewrite Expression

`Number\ of\ bags = 9 / {(8)/(3)`

`Number\ of\ bags = 9 * {(3)/(8)`

`Number\ of\ bags = {(9 * 3)/(8)`

`Number\ of\ bags = {(27)/(8)`

Convert to Mixed Fraction

`Number\ of\ bags = 3{(3)/(8)`

Hence, the number of bags needed to fill the flower pot is
`3{(3)/(8)`