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# Signature blend

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The Signature juice blend is 60% orange and 40% lemon, I have 10 quarts of blend X which is 80% orange and 20% lemon and 10 quarts of blend Y which is 20% orange and 20% lemon. How many quarts of blend X will I need to make 10 quarts of signature juice?

Dec 21, 2018

#1
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Cannot be done ...... with the two concentrations for X and Y given.

X  and Y BOTH have lemon concentration as 20%........combining them in ANY ratio will only result in Lemon 20%....signature is 40 % lemon and you cannot make that.

Dec 21, 2018
#2
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I apologize. Typo. The Y blend is 20% orange and 80% lemon

MacTyBoys  Dec 21, 2018
#3
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Let n be the number of quarts of Blend X  and (10- n) the number of quarts of Blend Y

Orange concentration in X  * n  +  orange concentration in Y * (10 - n)  =  .10 quarts at 60% orange

Lemon concentration in X * n  +  lemon concentraion in Y * (10-n) = 10 quarts at 40% lemon

We have this system

.80n +  .20 (10 -n)  =  10(.60)

.20n  + .80 (10-n)  = 10(.40)               simplify   [ multiply through by 10 ]

8n + 2(10-n) = 60

2n+ 8 (10 - n) = 40         simplify more

8n + 20 - 2n  = 60

2n+ 80 - 8n   = 40

6n + 20  = 60

-6n + 80 = 40

6n = 40

-6n = -40

Note that  n    =  40/6 qts   makes both equations true = quarts of Blend X = 6 + 2/3 qts

And Blend Y = 3 + 1/3  qts

Dec 21, 2018