Multiple choice

Two containers, A and B, have mixtures of chocolate and vanilla. Container A has a mixture in the ratio 2 : 3, and container B has a mixture in the ratio 4 : 5. How many kg of the mixture should be taken from each container to get a final mixture containing 8 kg of chocolate and 11 kg of vanilla?

  1. 9 kg from A and 20 kg from B

  2. 11 kg from A and 9 kg from B

  3. 10 kg from A and 9 kg from B

  4. 9 kg from A and 12 kg from B

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be kg from A and y be kg from B. Chocolate: (2/5)x + (4/9)y = 8. Vanilla: (3/5)x + (5/9)y = 11. Solving the system: 18x + 20y = 360 and 27x + 25y = 495. Multiplying first by 5 and second by 4: 90x + 100y = 1800 and 108x + 100y = 1980. 18x = 180, x = 10. Then 180 + 20y = 360, 20y = 180, y = 9.

AI explanation

Testing the given values, take 10 kg from container A, which provides 4 kg of chocolate and 6 kg of vanilla. Taking 9 kg from container B provides 4 kg of chocolate and 5 kg of vanilla. Combining these gives exactly 8 kg of chocolate and 11 kg of vanilla, matching the required final mixture.

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