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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?

MacTyBoys Dec 21, 2018

#1**+2 **

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.

ElectricPavlov Dec 21, 2018

#3**+2 **

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

CPhill Dec 21, 2018