Multiple choice

Emily has a 36-liter container filled with lemonade and limeade in the ratio of 5 : 7. How much lemonade should she add so that the resulting mixture contains lemonade and limeade in the ratio of 5 : 2?

  1. 33 liters

  2. 37.5 liters

  3. 41 liters

  4. 44.5 liters

  5. 49 liters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 36 liters total, ratio 5:7 means 15 liters lemonade and 21 liters limeade. Let x be the added lemonade; the new ratio is (15+x)/21 = 5/2. Solving 2(15+x) = 105 gives 30 + 2x = 105, so 2x = 75, x = 37.5.

AI explanation

In the initial 36-liter container, the quantities of lemonade and limeade are 5/12 and 7/12 of the total, which equals 15 liters and 21 liters respectively. Let the added lemonade be x liters, and set the new ratio as (15 + x) / 21 = 5 / 2. Solving this equation gives 30 + 2x = 105, so 2x = 75 and x = 37.5. She should add 37.5 liters of lemonade.

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