Question

How much of Brand A fruit punch must be mixed with 2 L of Brand B fruit punch to create a mixture containing 16% fruit juice?

Answer 1

To create a mixture containing 16% fruit juice, approximately 0.38 L of Brand A fruit punch must be mixed with 2 L of Brand B fruit punch.

Step-by-step explanation:

To solve this problem, let's assume that x represents the volume of Brand A fruit punch that needs to be mixed with 2 L of Brand B fruit punch. Since we want the mixture to contain 16% fruit juice, the amount of fruit juice in Brand A punch mixed with the amount of fruit juice in Brand B punch should equal 16% of the total volume of the mixture. We can set up the following equation:
(x)(100%) + (2 L)(0%) = (x + 2 L)(16%)
Simplifying the equation:
x + (0) = 0.16(x + 2 L)
Distributing the 0.16 on the right side of the equation:
x = 0.16x + 0.32 L
Subtracting 0.16x from both sides of the equation:
x - 0.16x = 0.32 L
Simplifying:
0.84x = 0.32 L
Dividing both sides of the equation by 0.84:
x = 0.32 L / 0.84
x ≈ 0.38 L