Question

A cafeteria worker needs to make a mixture of 100 liters of 50 percent solution of apple juice. How many liters of a 80 percent solution of apple juice and a 30 percent solution of apple juice are needed?

Answer 1

The Amount of 80% solution of Apple juice = 60 liters

The Amount of 30% solution of Apple juice = 40 liters

Explanation:

Given in the question as :

A cafeteria worker need to make 100 liters of of 50% solution of apple juice

Let for 80% solution of apple juice he need x liter

And for 30% solution of apple juice he need y liter

I,e x + y = 100

And 80% of x + 30% of y = 50% of (x + y)

Or 80% of x + 30% of y = 50% of x + 50 % of y

I.e (80% of x - 50% of x) = ( 50 % of y - 30% of y)

Or, 30% of x = 20% of y

∴ 3 x = 2 y

Or, x =
`(3)/(2)` y

∵ x + y = 100 ,

So ,
`(3)/(2)` y + y = 100

Or,
`(3y + 2y)/(2)` = 100

∴ 5y = 200

i.e y =
`(200)/(5)` = 40 liters

And x = 100 - 40 = 60 liters

Hence , The Amount of 80% solution of Apple juice = 60 liters

And The Amount of 30% solution of Apple juice = 40 liters Answer