Final answer:
To create a mixture containing 60% fruit juice by mixing Brand A fruit punch with 5 liters of grape juice, you need to add 8 liters of Brand A fruit punch.
Step-by-step explanation:
To determine how much of Brand A fruit punch, which contains 35% fruit juice, needs to be mixed with 5 liters of grape juice, we will set up a mixture problem to find a mixture containing 60% fruit juice. Let x represent the amount of fruit punch to be added to the grape juice.
Using the equation for a mixture, calculate the total amount of fruit juice from both parts:
0.35x (juice from Brand A fruit punch) + 5L (since grape juice is 100% fruit juice).
The mixture will be (x + 5) liters of punch after combining. We want the resulting mixture to have 60% fruit juice:
0.60(x + 5) (total amount of juice in the mixture).
Now, we equate the amount of juice from both parts to the amount in the final mixture:
0.35x + 5 = 0.60(x + 5).
Distribute the 0.60:
0.35x + 5 = 0.60x + 3.
Now, subtract 0.35x from both sides:
5 - 3 = 0.60x - 0.35x,
which simplifies to:
2 = 0.25x.
Dividing both sides by 0.25 gives us the amount of Brand A fruit punch required:
x = 2 / 0.25,
x = 8 liters.
Therefore, 8 liters of Brand A fruit punch is required to create the mixture with 60% fruit juice when mixed with 5 liters of grape juice.