Q:

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?

Accepted Solution

A:
80 liters of orange juice must be mixed.ExplanationLets assume, the amount of orange juice is [tex]x[/tex] liters. As the amount of mixture is 200 liters, so the amount of grapefruit juice will be: [tex](200-x)liters[/tex]Price of orange juice = 42¢ /liter , price of grapefruit juice = 32¢ /liter and the price of mixture = 36¢ /literSo,  total price of [tex]x[/tex] liters orange juice [tex]= 42x[/tex] ¢ , total price of [tex](200-x)[/tex] liters grapefruit juice [tex]=32(200-x)[/tex] ¢  and total price of 200 liters mixture [tex]= 200*36= 7200[/tex] ¢ Thus the equation will be ....[tex]42x+32(200-x)= 7200\\ \\ 42x+6400-32x=7200\\ \\ 10x=7200-6400\\ \\ 10x=800\\ \\ x= \frac{800}{10} = 80[/tex]So, the amount of orange juice to be mixed is 80 liters.