Multiple choice

A receptacle contains a blend of 240 ml of orange juice and 360 ml of apple juice. Sarah extracts 15% of the mixture and replaces it with an equivalent quantity of apple juice. She proceeds to repeat this sequence two more times. What percentage of apple juice comprises the ultimate composition of the mixture?

  1. 80.9%

  2. 89.18%

  3. 75.44%

  4. 79.18%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial apple juice = 360/600 = 60%. Each replacement removes 15% of the mixture and adds pure apple juice. After 3 cycles, the remaining original mixture is (0.85)^3 = 0.614125. The apple juice fraction is 1 - (0.4 * 0.614125) = 1 - 0.24565 = 0.75435, or 75.44%.

AI explanation

The initial mixture contains 360 ml of apple juice out of 600 ml, so the initial orange juice amount is 240 ml. Using the replacement formula, the final quantity of orange juice is 240 multiplied by (1 minus 0.15) cubed. This evaluates to 240 multiplied by 0.614125, which equals 147.39 ml of orange juice. The final apple juice quantity is 600 minus 147.39, equaling 452.61 ml, meaning apple juice comprises 75.44 percent of the ultimate composition.

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