Ugly word problems 10pt for best answer =]?

Question

1) How much orange juice at 42¢ a liter should be mixed with grapefruit juice worth 32¢ a liter to make 200 liters of a mixture worth 36¢ a liter?

If x represents the amount of orange juice used, then which of the following expressions represents the total cost of the grapefruit juice used?

2)How much orange juice at 42¢ a liter should be mixed with grapefruit juice worth 32¢ a liter to make 200 liters of a mixture worth 36¢ a liter

Answer 1

If x is the amount of orange juice used, then 200-x is the amount of grapefruit juice used and (200-x)*32¢ is the total cost of the grapefruit juice used. Or 32¢*(200-x).  Or $0.32(200-x), etc.

42*(x)+32*(200-x)=36*200

42x+6400-32x=7200

10x+6400=7200

10x=800

x=80 liters (of orange juice)

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Answer 2

Let X be the amount of orange juice and G the amount of grapefruit juice.

X + G = 200

( .42 ) X + ( .32 ) G = ( .36 ) ( 100 )

The first equation tells us that G = 200 - X

( .42 ) X + ( .32 ) ( 200 - X ) = 36

.42 X + 32 - .32 X = 36

.10 X = 8  

X = 80 liters

You need 80 liters of orange juice and 120 liters of grapefruit juice.

CHECK:

( .42 ) ( 80 ) + ( .32 ) ( 120 ) = 72 = ( .36 ) ( 200 )