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.

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 ....

$42x+32(200-x)= 7200\\ \\ 42x+6400-32x=7200\\ \\ 10x=7200-6400\\ \\ 10x=800\\ \\ x= \frac{800}{10} = 80$

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