Multiple choice

In the realm of fruit beverages, a vendor is faced with the task of concocting the perfect blend. In one container, there is a mixture consisting of 30% orange juice, with the remaining portion being apple juice. The second container, on the other hand, holds a solution containing 40% orange juice and remaining is apple juice. Determine the quantities from each container that need to be combined to yield 15 liters of juice, maintaining a desired ratio of 4 parts orange juice to 7 parts apple juice. What volumes from each container should be mixed to achieve this harmonious blend?

  1. 5 liters, 10 liters

  2. 4 liters, 11 liters

  3. 5.45 liters, 9.55 liters

  4. 6.54 liters, 8.46 liters

  5. 3.54 liters, 10.46 liters
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be volume from container 1 and y be volume from container 2. x + y = 15. Orange juice: 0.3x + 0.4y = (4/11) * 15. Solving the system: x + y = 15 and 0.3x + 0.4y = 5.4545. 0.3x + 0.4(15-x) = 5.4545 -> 6 - 0.1x = 5.4545 -> 0.1x = 0.5455 -> x = 5.455, y = 9.545.

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