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# A container holds 4 quarts of alcohol and 4 quarts of water.

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A container holds 4 quarts of alcohol and 4 quarts of water. [#permalink]  04 Dec 2017, 04:59
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A container holds 4 quarts of alcohol and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume?

A. 4/3
B. 5/3
C. 7/3
D. 8/3
E. 10/3

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Re: A container holds 4 quarts of alcohol and 4 quarts of water. [#permalink]  04 Dec 2017, 14:09
Bunuel wrote:
A container holds 4 quarts of alcohol and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume?

A. 4/3
B. 5/3
C. 7/3
D. 8/3
E. 10/3

Here
$$\frac{4 quarts of Alcohol}{4 quarts of water}$$

we need to add water to above solution to make it equal to = $$\frac{3 parts of Alcohol}{5 parts of water}$$
Let w= quarts of water required

Total quarts of water = (4 + w)

Therefore we can re write as -

$$\frac{4 quarts of Alcohol}{(4 quarts of water + w)}$$ = $$\frac{3 parts of Alcohol}{5 parts of water}$$(since we need to add w to make the ratio equal to 3/5)

or $$\frac{4}{(4+w)}$$ =$$\frac{3}{5}$$

or w =$$\frac{8}{3}$$
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Re: A container holds 4 quarts of alcohol and 4 quarts of water. [#permalink]  05 Jan 2018, 07:46
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Expert's post
Bunuel wrote:
A container holds 4 quarts of alcohol and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume?

A. 4/3
B. 5/3
C. 7/3
D. 8/3
E. 10/3

We can create the following equation in which n = the added water:

4/(4 + n) = 3/5

20 = 12 + 3n

8 = 3n

8/3 = n

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Jeffery Miller

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Re: A container holds 4 quarts of alcohol and 4 quarts of water.   [#permalink] 05 Jan 2018, 07:46
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