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A certain bag contains a mixture of nuts and raisins, in the ratio of

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A certain bag contains a mixture of nuts and raisins, in the ratio of [#permalink]

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New post 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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A certain bag contains a mixture of nuts and raisins, in the ratio of [#permalink]

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New post 27 Dec 2017, 19:04
ansch wrote:
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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A certain bag contains a mixture of nuts and raisins, in the ratio of   [#permalink] 27 Dec 2017, 19:04
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