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?

Answer 1

80 liters of orange juice must be mixed.

Step-by-step explanation

Lets assume, the amount of orange juice is
`x` liters.

As the amount of mixture is 200 liters, so the amount of grapefruit juice will be:
`(200-x)liters`

Price of orange juice = 42¢ /liter , price of grapefruit juice = 32¢ /liter and the price of mixture = 36¢ /liter

So, total price of
`x` liters orange juice
`= 42x` ¢ ,

total price of
`(200-x)` liters grapefruit juice
`=32(200-x)` ¢ and

total price of 200 liters mixture
`= 200*36= 7200` ¢

Thus the equation will be ....

`42x+32(200-x)= 7200\\ \\ 42x+6400-32x=7200\\ \\ 10x=7200-6400\\ \\ 10x=800\\ \\ x= (800)/(10) = 80`

So, the amount of orange juice to be mixed is 80 liters.