We have been given that Mason plans to repaint some classroom bookcases. He has [tex]5\frac{5}{7}[/tex] 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.
[tex]\text{Bookcases that can be painted}=\frac{\text{Total amount of paint}}{\text{Amount of paint needed to paint each bookcase}}[/tex]
Let us convert [tex]5\frac{5}{7}[/tex] into mixed fraction:
[tex]5\frac{5}{7}\Rightarrow \frac{7\cdot 5+5}{7}=\frac{35+5}{7}=\frac{40}{7}[/tex]
[tex]\text{Bookcases that can be painted}=\frac{\frac{40}{7}}{\frac{1}{2}}}[/tex]
Using property [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}[/tex], we will get:
[tex]\text{Bookcases that can be painted}=\frac{40\cdot 2}{7\cdot 1}[/tex]
[tex]\text{Bookcases that can be painted}=\frac{80}{7}[/tex]
[tex]\text{Bookcases that can be painted}=11\frac{3}{7}[/tex]
Therefore, Mason will be able to repaint [tex]11\frac{3}{7}[/tex] bookcases.
