A 2 gallon mixture of fruit juice is 15% orange juice. You want the mixtures to be 32% orange juice

orange-juice

#1

A 2 gallon mixture of fruit juice is 15% orange juice. You want the mixtures to be 32% orange juice. How much pure orange juice should you add to the mixture?

Answer:

I answered this through the sesh but if anyone also wants the answer:

.15(2) + x = .32(2+x)
we’ll turn that into fraction
3/10 + x = 8/25(2+x)
now we multiply 8/25 by 2 & x
3/10 + x = 16/25 + 8/25x
-3/10 on both sides of the equation
x = 16/25 + 8/25x -3/10
Now we’ll substract 8/25x on both sides
x - 8/25x = 16/25 - 3/10
So we want the denominators to be equal on both sides so :
25/25x - 8/25x = 32/50 - 15/50
Now we can solve
17/25x = 17/50
Isolate x:
x = 17/50 * 25/17 (we multiply by the reciprocal)
x = .34 * 25 = 8.5 / 17 = .5 or 50% or 1/2

So yeah 1/2 gallons