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Problem 583

AMC 12 late, AIME early

Algebra Difficulty 5.0 Find the answer

A1. Maja filled two identical pitchers with lemonade, so that the first pitcher was filled to $\frac{1}{3}$ , and the second to $\frac{2}{5}$ . Then she added water to both pitchers until they were full. Finally, she poured the contents of both pitchers into a larger bowl, without any liquid spilling over the edge of the bowl. What fraction of the liquid in the bowl is lemonade?
(A) $\frac{1}{8}$
(B) $\frac{3}{16}$
(C) $\frac{11}{30}$
(D) $\frac{11}{19}$
(E) $\frac{11}{15}$

Your answer

Official solution

A1. Let the amount of liquid that one basket can hold be denoted by $e$ . Then, in the jug, there is $\frac{1}{3} e + \frac{2}{5} e = \frac{11}{15} e$ of lemonade out of a total of $2 e$ liquid. Therefore, the lemonade represents $\frac{\frac{11}{15} e}{2 e} = \frac{11}{30}$ of the liquid in the jug.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.