AbdurRakib wrote:

Two bottles are partially filled with water. The larger bottle currently holds \(\frac{1}{3}\) of its capacity. The smaller bottle, which has \(\frac{2}{3}\) of the capacity of the larger bottle, currently holds \(\frac{3}{4}\) of its capacity.If the contents of the smaller bottle are poured into the larger bottle, the larger bottle will be filled to what fraction of its

capacity?

Let \(L\) be the capacity of the larger bottle

Let \(l\) be the current capacity of the larger bottle. \(l = \frac{1}{3}L\)

Let \(S\) be the capacity of the smaller bottle. \(S = \frac{2}{3}L\)

Let \(s\) be the current capacity of the smaller bottle. \(s = \frac{3}{4}S\)

Question: What is \(l + s\)

First get \(s\) in terms of \(L\)

\(s = \frac{3}{4} \times \frac{2}{3}L = \frac{1}{2}L\)

\(s + l = (\frac{1}{2} + \frac{1}{3})L = \frac{5}{6}L\)

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