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Re: Two mixtures A and B contain milk and water in the ratios [#permalink]

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15 Jun 2016, 05:53

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Re: Two mixtures A and B contain milk and water in the ratios [#permalink]

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02 Aug 2016, 02:37

bmwhype2 wrote:

Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?

A. 144 B. 122.5 C. 105.10 D. 72 E. 134

I tried two approaches.one in which i convereted 40% to fraction form and the second in which i converted 2/7 to % form.The later method yielded the correct OA.why???

Re: Two mixtures A and B contain milk and water in the ratios [#permalink]

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06 Sep 2016, 14:10

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bmwhype2 wrote:

Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?

A. 144 B. 122.5 C. 105.10 D. 72 E. 134

When solving some mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED.

First recognize that if mixture A has a milk to water ratio of 2:5, then the mixture is 2/7 milk. Also recognize that if mixture B has a milk to water ratio of 5:4, then the mixture is 5/9 milk.

Start with 90 gallons of mixture B, which is 5/9 milk: When we draw this with the ingredients separated, we see we have 50 gallons of milk in the mixture.

Next, we'll let x = the number of gallons of mixture A we need to add. Since 2/7 of mixture A is milk, we know that (2/7)x = the volume of MILK in this mixture:

At this point, we can ADD the two solutions (PART BY PART) to get the following volumes:

Since the RESULTING mixture is 40% milk (i.e., 40/100 of the mixture is milk), we can write the following equation: [50 + (2/7)x]/(90 + x) = 40/100 Simplify to get: [50 + (2/7)x]/(90 + x) = 2/5 Cross multiply to get: 5[50 + (2/7)x] = 2(90 + x) Expand: 250 + (10/7)x = 180 + 2x Subtract 180 from both sides to get: 70 + (10/7)x = 2x Multiply both sides by 7 to get: 490 + 10x = 14x Rearrange: 490 = 4x Solve: x = 490/4 = 245/2 = 122.5

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