Question

A cafe uses $2\frac{1}{2}$ cups of milk for a vanilla milkshake and $3\frac{1}{3}$ cups of milk for a chocolate milkshake. If the size of the milkshakes is halved, find the difference in the quantity of milk in both the milkshakes.

• A. $\frac{10}{12}$ cups
• B. $\frac{5}{11}$ cups
• C. $\frac{5}{12}$ cups
• D. $\frac{5}{6}$ cups

Answer 1

The correct option is C $\frac{5}{12}$ cups

Quantity of milk in the new vanilla milkshake $=\frac{1}{2}\times 2\frac{1}{2}$

Quantity of milk in the new chocolate milkshake $=\frac{1}{2}\times 3\frac{1}{3}$

Difference in the quantity of milk $=\frac{1}{2}\times 3\frac{1}{3}-\frac{1}{2}\times 2\frac{1}{2}$

$=\frac{1}{2}\times (3\frac{1}{3}-2\frac{1}{2})\text{[Distributive property]}$

$=\frac{1}{2}\times (\frac{9+1}{3}-\frac{4+1}{2})$

$=\frac{1}{2}\times (\frac{10}{3}-\frac{5}{2})$

$=\frac{1}{2}\times \left(\frac{20-15}{6}\right)$

$=\frac{1}{2}\times \frac{5}{6}$

$=\frac{5}{12}$ cups

Note: If we would have taken Vanilla - chocolate in place of chocolate - vanilla, the result would have been the same but with a negative sign i.e $-\frac{5}{12}$. The difference is the absolute value so the final answer would have been still as $\frac{5}{12}$ cups.