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Two mixtures A and B contain milk and water in the ratios

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

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

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New post 15 Jun 2016, 11:44
let x=gallons of A to be mixed
2/7*x+5/9*90=.4(x+90)
x=490/4=122.5 gallons

Last edited by gracie on 23 Dec 2016, 13:32, edited 1 time in total.
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Re: Two mixtures A and B contain milk and water in the ratios [#permalink]

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

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New post 02 Aug 2016, 05:34
How abt this approach.

of all the options provided only 122.5 is divisible by 7 ie. ratio of A is 2:5, so the mixture need to be in multiple of 7.
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Re: Two mixtures A and B contain milk and water in the ratios [#permalink]

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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:
Image
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:
Image

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

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

Answer:
[Reveal] Spoiler:
B


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

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New post 23 Dec 2016, 08:03
2x+50/5x+40=4/6, find x, then don't get into decimals, approx 17.something then 2(17)+5(17)= approx 122
Re: Two mixtures A and B contain milk and water in the ratios   [#permalink] 23 Dec 2016, 08:03

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