document.write( "Question 1011852: I'm a 66 year old man with a debate with my wife. I say the mixture would be 4 to 1 she disagrees. A 40% solution is to be mixed with water how much water is needed to make the solution 10%? \n" ); document.write( "

Algebra.Com's Answer #627663 by MathTherapy(10552) $\"\"$ $\"About$

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I'm a 66 year old man with a debate with my wife. I say the mixture would be 4 to 1 she disagrees. A 40% solution is to be mixed with water how much water is needed to make the solution 10%?
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Sorry, sir, you're wrong! I assume you merely did a ratio of 40%:10% to get 4:1, but it doesn't work like that 
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document.write( "I don't know what your wife's ratio is, but yours is incorrect.\r
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document.write( "Let original amount of solution be S, and amount of water to add, W
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document.write( "Let's assume that the S units of solution contains .6S water 
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document.write( "Water + water = water
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document.write( "Then we get: .6(S) + W = .9(S + W) ---- Amounts of water in original solution and new solution are: .6, and .9, respectively 
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document.write( ".6S + W = .9S + .9W
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document.write( "W – .9W = .9S - .6S
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document.write( ".1W = .3S
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document.write( "W, or amount of water to add = , or 3S. 
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document.write( "This means that the amount of water to be added is 3 times the amount of the original solution. \r
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document.write( "Now, the solution consists of 4S (S + 3S), of which 3S units of water were added to the original .6S units of water, which results in 3.6S units of water.
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document.write( "This makes the ratio: 3.6S:.4S, or  \n" );
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