Question

How much of Brand A fruit punch (30% fruit juice) must be mixed with 9 L of Brand B fruit punch (40% fruit juice) to create a mixture containing 36% fruit juice?

a) 6 L of Brand A fruit punch
b) 3 L of Brand A fruit punch
c) 4 L of Brand A fruit punch
d) 5 L of Brand A fruit punch

Answer 1

To create a mixture with 36% fruit juice, 6 L of Brand A fruit punch, which has 30% fruit juice, must be mixed with 9 L of Brand B fruit punch that contains 40% fruit juice.

Step-by-step explanation:

To determine how much of Brand A fruit punch needs to be mixed with 9 L of Brand B to get a 36% fruit juice mixture, we need to set up an equation that represents the total amount of fruit juice in the final mixture. Let x represent the volume in liters of Brand A fruit punch needed.

The amount of fruit juice in Brand A is 0.30x (since Brand A has 30% fruit juice) and the amount of fruit juice in Brand B is 0.40×9 (since Brand B has 40% fruit juice and we have 9 liters of it). The final mixture has 36% fruit juice, which is represented by the equation:

0.30x + 0.40×9 = 0.36(x + 9)

Solving for x, we have:

0.30x + 3.6 = 0.36x + 3.24

0.06x = 0.36

x = 0.36 / 0.06

x = 6

So, 6 L of Brand A fruit punch is needed.