Question 214281

OK
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