Question

To create a breakfast beverage, cherry juice in two concentrations, 25% and 50%, must be combined into a solution that will be mixed with another type of juice to produce the beverage. If 70 gallons of 25% juice is used, how many gallons of the 50% juice must be used to obtain a 40% cherry juice solution?

Answer 1

Note we are only interested in the cherry juice solution before the addition of the third juice. So ignore the third juice making up the beverage.
Let the quantity of juice with 25% be A.
Let the quantity of juice with 50% be B
then 0.25A +0.5B=0.4(A+B)
now A=70 gallons
17.5+0.5B=0.4(70+B)
=28+0.4B
0.1B=10.5
B=105 gallons.

Answer 2

ok thank you so how would I set up the equation on this one?

A solution of 78% alcohol is to be mixed with a solution of 23% alcohol to form 165 L of a 58% solution. How many liters of the 78% solution must be used?