Discussion
A container of milk was \(\frac{3}{4}\) full. When 5 bottles of milk were taken out and 3 bottles of milk were poured into it, it was \(\frac{2}{3}\) full. How many bottles of milk can the container contain ?
Answer: B
The container holds 24 bottles of milk.
Let the capacity be C bottles. Taking out 5 bottles and pouring in 3 is a net loss of 2 bottles, which takes the level from three-quarters to two-thirds:
\[ \begin{aligned} \tfrac{3}{4}C - 2 &= \tfrac{2}{3}C \\ \tfrac{1}{12}C &= 2 \\ C &= 24 \end{aligned} \]
Check: three-quarters of 24 is 18; after losing 2 bottles it holds 16, which is two-thirds of 24.
12 comes from treating the net change as 1 bottle, and 20 and 15 give non-whole quarter or third fills, so they cannot fit.
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