Bunuel wrote:
Rice mixture A is 25 percent brown rice and 75 percent wild rice by weight; and rice mixture B is 40 percent brown rice and 60 percent white rice by weight. If a blend of mixture A and mixture B contains 30 percent brown rice by weight, what percent of the weight of the blend is mixture A?
(A) 32 1/2%
(B) 33 1/3%
(C) 50%
(D) 65%
(E) 66 2/3%
Another approach: track on brown rice only,
use a weighted average, and derive percent of
A in final blend from that equation.
Wild rice and white rice do not matter in this equation.
The percent of A in the resultant blend depends
on the ratio of A to B.
A and B have brown rice in common.
That commonality will yield the ratio of A to B
in the final blend, which in turn will yield the percent of
A in the final blend.
Set up a very easy weighted average that tracks on brown rice.
In terms of brown rice,
BR:
(% of BR in A) + (% of BR in B) = % of BR in blend (A + B)
%\(A\) + %\(B\) = %\((A + B)\)
\(.25A + .40B = .30(A + B)\)
\(.25A + .40B = .30A + .30B\)
\(.10B = .05A\)
\(10B = 5A\)
\(\frac{A}{B} = \frac{10}{5} = \frac{2}{1} = \frac{2x}{1x}\)A is what percent of the resultant blend?
\(\frac{A}{A+B} * 100\)
\((\frac{2x}{2x + 1x} * 100)=(\frac{2x}{3x}* 100)=\)
\(.667 * 100 = 66\frac{2}{3}\) percent
Answer E
*
You can set this equation up without decimals from the start. A and B maintain the same ratio. Thus:
\(25A + 40B = 30(A + B)\) _________________
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