Question

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?

0.32x
0.32(200 - x)
0.32(x + 200)

Answer 1

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

Cost of grapefruit per liter = 32

Cost of orange juice per liter= 42

Total quantity of mixture = 200 liters

Let the quantity of orange juice be x

So, the quantity of grapefruit juice be 200-x

So, the total cost of the grapefruit juice used will be

$0.32(200-x)$

According to question,

$0.32(200-x)+0.42x=200\times 0.36\\\\64-0.32x+0.42x=72\\\\0.42x-0.32x=72-64\\\\0.1x=8\\\\x=80\\\\\text{ So, the amount of grapefruit juice will be }=200-80=120$

Hence, Second option is correct.

Answer 2

X = the amount of orange juice that still has to be mixed


If it says that the total of the juice will be 200 liters, then (200-x) = the amount of grapefruit juice that still needs to be mixed.


The grapefruit juice amount would be: 200 - 80 = 120 liters