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27 Dec 2017, 13:39
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A certain bag contains a mixture of nuts and raisins, in the ratio of 3:2, nuts to raisins by weight. If 15 pounds of nuts are removed, and are replaced with 20 pounds of raisins, so that the new ratio is 3:4, how many pounds of raisins were in the original mixture?
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27 Dec 2017, 19:04
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ansch
A certain bag contains a mixture of nuts and raisins, in the ratio of 3:2, nuts to raisins by weight. If 15 pounds of nuts are removed, and are replaced with 20 pounds of raisins, so that the new ratio is 3:4, how many pounds of raisins were in the original mixture?
ansch , please post answer choices, OA, and source.1) Original ratio with a multiplier
\(\frac{N}{R} = \frac{3x}{2x}\)
2) Set up the equation
15 pounds of nuts are removed, and are replaced with 20 pounds of raisins (20 pounds of raisins are added)
\(\frac{3x - 15}{2x +\\
20}=\) (LHS)
And the new ratio is \(\frac{3}{4}\) (RHS)
\(\frac{3x - 15}{2x +\\
20}\\
= \frac{3}{4}\)
\(4(3x - 15) = 3(2x + 20)\)
\(12x - 60 = 6x + 60\)
\(6x = 120\)
\(x = 20\)
So the multiplier for the original ratio is x = 20
3) How many pounds of raisins in the original mixture?
x = 20
Raisins = 2x = (2)(20) =
40 pounds of raisins in original mixture
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04 Dec 2019, 02:07
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