Question

Mason plans to repaint some classroom bookcases. He has 5 5/7 gallons of paint. All of the bookcases are the same size and each requires 1/2 gallon of paint. How many bookcases will the custodian be able to repaint with that amount of paint?

Answer 1

We have been given that Mason plans to repaint some classroom bookcases. He has
`5(5)/(7)` gallons of paint. All of the bookcases are the same size and each requires 1/2 gallon of paint.

We are asked to find the number of bookcases that Mason will be able to repaint with available amount of paint.

`\text{Bookcases that can be painted}=\frac{\text{Total amount of paint}}{\text{Amount of paint needed to paint each bookcase}}`

Let us convert
`5(5)/(7)` into mixed fraction:

`5(5)/(7)\Rightarrow (7\cdot 5+5)/(7)=(35+5)/(7)=(40)/(7)`

`\text{Bookcases that can be painted}=((40)/(7))/((1)/(2))}`

Using property
`((a)/(b))/((c)/(d))=(ad)/(bc)`, we will get:

`\text{Bookcases that can be painted}=(40\cdot 2)/(7\cdot 1)`

`\text{Bookcases that can be painted}=(80)/(7)`

`\text{Bookcases that can be painted}=11(3)/(7)`

Therefore, Mason will be able to repaint
`11(3)/(7)` bookcases.