Question 657343: Juice-O-Rama is a refreshment stand specializing in a fruit drink mixture of orange juice and prune juice. The orange juice costs $1.20 per liter and the prune juice costs $1.40 per liter. If they need 8 liters of the final drink at a cost of $1.24 per liter, how many liters of each juice will they need to make their specialty drink?
I don't really know how to start, but I put x as the liters of orange juice and y as the liters of prune juice. I set x+y=8, but this is where I get confused
Answer by kevwill(135)   (Show Source):
You can put this solution on YOUR website! You're off to a good start.
Let x = liters of orange juice
and y = liters of prune juice.
Then x + y = 8.
Since each liter of orange juice costs $1.20 and each liter of prune juice costs $1.40, the total cost of the mixture is 1.20x + 1.40y.
We are given that the final drink costs $1.24 per liter, or $1.24*8 = $9.92 for the entire 8 liters. This gives us our second equation:
1.20x + 1.40y = 9.92
We now have two equations in two unknowns:
x + y = 8
1.2x + 1.4y = 9.92
We'll use substitution. From the first equation, move x to the right (by subtracting x from each side), giving
y = 8 - x
Substituting for y in the second equation gives
1.2x + 1.4(8-x) = 9.92
Expanding:
1.2x + 11.2 - 1.4x = 9.92
Subtract 11.2 from each side and regroup:
(1.2x - 1.4x) = 9.92 - 11.2
Combining terms:
-0.2x = -1.28
Dividing both sides by -0.2:
x = -1.28/-0.2 = 6.4
From our first substitution,
y = 8 - 6.4 = 1.6
So the final drink contains 6.4 liters of orange juice and 1.6 liters of prune juice.
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