Question

Beth mixed together 2 L of Brand A fruit drink and 6 L of Brand B fruit drink which contains 15% fruit juice. Find the percent of fruit juice in Brand A if the mixture contained 25% fruit juice​

Answer 1

The percentage of fruit juice in Brand A is 55%, calculated by setting up an equation from the total fruit juice content of the final mixture.

Step-by-step explanation:

To find the percent of fruit juice in Brand A, we can set up an equation based on the final mixture containing 25% fruit juice. Let's denote the unknown percent of fruit juice in Brand A as x. Since there are 2 L of Brand A and 6 L of Brand B in the mixture, we have a total volume of 8 L of mixed fruit drink.

Brand B contains 15% fruit juice, and there are 6 L of it. So, Brand B contributes 0.15 × 6 L = 0.9 L of fruit juice. The mixture has 25% fruit juice, which means 0.25 × 8 L = 2 L of fruit juice in total. Since 0.9 L of this comes from Brand B, the remaining fruit juice must come from Brand A:

0.25 × 8 L - 0.9 L = 2 L - 0.9 L = 1.1 L

This 1.1 L of fruit juice is 25% of the mixture and came from the 2 L of Brand A. To find x, the percent of fruit juice in Brand A, we use the equation:

x × 2 L = 1.1 L

Divide both sides by 2 to solve for x:

x = 1.1 L / 2 L = 0.55

Converting this to a percentage:

x = 55%

Therefore, Brand A contains 55% fruit juice.