SOLUTION: How many quarts of pure orange juice should micheal add to a 10% orange drink create 6 quarts of a 40% orange juice mixture? Let p represent the number of quarts of pure orange jui
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Question 214281: How many quarts of pure orange juice should micheal add to a 10% orange drink create 6 quarts of a 40% orange juice mixture? Let p represent the number of quarts of pure orange juice he should add to the orange drink Answer by ptaylor(2198) (Show Source):
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Let p=number of qts of pure orange juice needed
First, we'll solve the problem by dealing with the orange juice and then we'll solve it by dealing with the other ingredients in the drink.
Now we know that the amount of pure orange juice added(p) plus the amount of pure orange juice in the 10% drink ((0.10(6-p)) has to equal the amount of pure orange juice in the final mixture (0.40)(6). So our equation to solve is:
p+0.10*(6-p)=(0.40)*6 get rid of parens and simplify
p+0.60-0.10p=2.4 subtract 0.60 from each side
p-0.10p+0.60-0.60=2.4-0.60 collect like terms
0.90p=1.8
divide each side by 0.90
p=2 qts-----------------------number of qts of pure orange juice needed
Now let's solve the problem by dealing with the other ingredients
As before, let p=number of qts of pure orange juice needed
Now we know that the amount of other ingredients in the pure orange juice added(0) plus the amount of other ingredients in the 10% drink ((0.90(6-p)) has to equal the amount of other ingredients in the final mixture (0.60)(6). So our equation to solve is:
0.90(6-p)=0.60*60
5.4-0.90p=3.6 subtract 5.4 from each side
-0.90p=-5.4+3.6
-0.90p=-1.8 divide each side by -0.90
p=2 qts ---same as before
Hope this helps----ptaylor
