Question 218863: This is a real question I need answered. I have 1 gallon of grape juice with 20% sugar content. I have another gallon of grape juice that has 68% sugar content. How much of the 68% sugar juice do I add to the 20% sugar juice to get a Juice that has 24% sugar content. Please help if you can.
Thanks,
Jim
Found 3 solutions by RAY100, ptaylor, stanbon:
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! Let x = amount added in gallons
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.2*1 + .68*x = .24(1+x)
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.2 +.68x =.24 +.24x
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.44x = .04
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x=.091 gallons
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check,,,.2 +.68*.091 =1.091*.24
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.2618 = .2618,,,,ok
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Answer by ptaylor(2198)  (Show Source):
You can put this solution on YOUR website! OK.
Let x=amount of 68% juice that is needed
Now we know that the amount of pure sugar in the 20% juice (0.20*1) plus the amount of pure sugar in the 68% juice that is added(0.68x) has to equal the amount of pure sugar in the final mixture (0.24(1+x)), so our equation to solve is:
0.20*1+0.68x=0.24(1+x) get rid of parens
0.20*1+0.68x=0.24+0.24x or
0.20+0.68x=0.24+0.24x subtract 0.24x and also 0.20 from each side of the equation
0.20-0.20+0.68x-0.24x=0.24-0.20 combine like terms
0.44x=0.04 divide each side by 0.44
x=0.091 gal-------------amount of 68% juice that is needed
CK
0.20*1 +0.091*0.68=(1.091)*0.24
0.20+0.062=0.262
0.262=0.262
Hope this helps---ptaylor
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! I have 1 gallon of grape juice with 20% sugar content. I have another gallon of grape juice that has 68% sugar content. How much of the 68% sugar juice do I add to the 20% sugar juice to get a Juice that has 24% sugar content.
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Equation:
sugar + sugar = sugar
0.20(1) + 0.68(x) = 0.24(1+x)
Multiply thru by 100 to get:
20 + 68x = 24 + 24x
44x = 4
x = 1/11 gallon (amt. of 68% grape juice needed in the mixture)
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1/11 gal. = 0.091 gallons
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Cheers,
Stan H.
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