Bunuel wrote:
The ratio of the volumes of two empty pools is 5 : 3. If the smaller pool is filled and emptied into the larger pool, what is the ratio of filled volume to empty volume in the pools?
A. 1 : 4
B. 2 : 5
C. 3 : 5
D. 3 : 8
E. 5 : 8
If a ratio approach is used, one way to avoid confusion: the ratio of the two empty pools' volumes needs to have its parts
totaled.
If \(\frac{Big}{Small} = \frac{5x}{3x}\), then total empty capacity is \(8x\).
If \(3x\) (the capacity of the small pool) is put into the big pool, the filled ratio/fraction is not \(\frac{3x}{5x}\)
The filled ratio/fraction is \(\frac{3x}{8x}\) (i.e., \(\frac{3}{8}\) of total capacity is filled, 3 of 8 parts are filled)
Then
(Total Empty Capacity) - (Fraction Filled) =
(Fraction NOT filled, i.e., Fraction that is Empty)
\((\frac{8x}{8x} - \frac{3x}{8x}) = \frac{5x}{8x}=\frac{5}{8}\) of total capacity is NOT filled. Fraction that is empty = \(\frac{5}{8}\)
Ratio of filled to empty:
\(\frac{\frac{3}{8}}{\frac{5}{8}} = \frac{3}{8}*\frac{8}{5}=\frac{3}{5}\)
Answer C
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