Given that each of Mike's mug holds
[tex]\frac{4}{5}\text{ of a pint of liquid}[/tex]This implies that
[tex]1\text{ mug holds }\frac{4}{5}\text{ pints}[/tex]Let x mugs in total, hold 4 pints of chocolate.
This implies that
[tex]x\text{ mugs hold 4 pints}[/tex]Since each friend is assigned a mug, the total number of mugs is the same as the total number of friends.
Thus,
[tex]\begin{gathered} 1\text{ mug }\Rightarrow\frac{4}{5}\text{ pints} \\ x\text{ mug }\Rightarrow4\text{ pints} \\ \end{gathered}[/tex]
By cross-multiplication, we have
[tex]\begin{gathered} 1\text{ mug }\times\text{ 4 pints = }\frac{4}{5}\text{ pints }\times\text{ x mug} \\ \end{gathered}[/tex]Make x the subject of the formula
[tex]\begin{gathered} x=\frac{1\text{ mug }\times\text{ 4 pints}}{\frac{4}{5}\text{ pints}} \\ x=\text{ 5} \end{gathered}[/tex]Thus, 5 friends will get hot chocolate
