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

Answer:

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

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

Step-by-step 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 =$\frac{3}{2}$ y

∵  x + y = 100 ,

So , $\frac{3}{2}$ y + y = 100

Or,  $\frac{3y + 2y}{2}$ = 100

∴   5y = 200

i.e y = $\frac{200}{5}$ = 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