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

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Joined: 27 Dec 2017
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A certain bag contains a mixture of nuts and raisins, in the ratio of  [#permalink]

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27 Dec 2017, 12:39
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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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27 Dec 2017, 18:04
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?

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 &nbs [#permalink] 27 Dec 2017, 18:04
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