Discussion
A tank of water was \(\frac{5}{7}\) full. When 22 buckets of water was taken out and 11 buckets of water was poured into it, it was \(\frac{2}{5}\) full. How many total buckets of water can the tank contain ?
Answer: D
The tank holds 35 buckets.
Let the tank hold T buckets. Taking out 22 and pouring in 11 is a net removal of 11 buckets, which lowered the level from \(\frac{5}{7}\) to \(\frac{2}{5}\):
\[ \begin{aligned} \tfrac{5}{7}T - \tfrac{2}{5}T &= 11 \\ \tfrac{25 - 14}{35}T &= 11 \\ T &= 35 \end{aligned} \]
Check: \(\frac{5}{7}\) of 35 is 25, and \(25 - 11 = 14\), which is \(\frac{2}{5}\) of 35. The other capacities do not divide evenly by both 7 and 5.
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