Question 124194: This a mixture problem
How much orange juice at $0.42/liter should be mixed be grapefruit juice worth $0.32/liter to make 200 liters of a mixture worth $0.36/liter?
I'd appreciate your help. Thanks!
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
Let x=amount of orange juice needed
and $0.42x=value of the orange juice
Then 200-x=amount of grapefruit juice needed
and $0.32(200-x)=value of the grapefruit juice
Now it stands to reason that the value of the juices before they are mixed together has to equal the value of the final mixture which is: $0.36*200. So our equation to solve is:
$0.42x+$0.32(200-x)=$0.36*200 get rid of parens
$0.42x+64-$0.32x=72 subtract 64 from both sides
$0.42x-$0.32x+64-64=72-64 collect like terms
$0.10x=8 divide both sides by $0.10
x=80 liters-----------------amount of orange juice needed
200-x=200-80=120 liters----------------amount of grapefruit juice needed
CK
80*$0.42+120*$0.32=$0.36*200
33.6+38.4=72
72=72
Actually, we could also solve this problem using two unknowns:
Let x=amount of orange juice needed
And let y=amount of grapefruit juice needed
Then x+y=200------------------------eq1
and$0.42x+$0.32y=$0.36*200---------------eq2
Now if we substitute y=200-x from eq1 into eq2, guess what, we come out with the exact equation as before.
Hope this helps---ptaylor
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