Question

How much of Brand A fruit punch (35%

fruit juice) must be mixed with 5 L of
grape juice to create a mixture containing
60% fruit juice?

Answer 1

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.