Multiple choice

The ratio of wheat to rice in container A is 2 : 3 and that in container B is 3 : 7. What quantities (in kg) must be taken from A and B, respectively to form a mixture containing 5 kg of wheat and 11 kg of rice?

  1. 6, 10

  2. 4, 12

  3. 2, 14

  4. 8, 8

  5. 5, 11
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be kg from A and y be kg from B. Wheat: (2/5)x + (3/10)y = 5. Rice: (3/5)x + (7/10)y = 11. Multiply first by 2: 0.8x + 0.6y = 10. Multiply second by 2: 1.2x + 1.4y = 22. Solving the system: 4x + 3y = 50 and 6x + 7y = 110. Multiply first by 7 and second by 3: 28x + 21y = 350 and 18x + 21y = 330. Subtracting gives 10x = 20, so x = 2. Then 8 + 3y = 50, 3y = 42, y = 14.

AI explanation

Let the quantities taken from container A and container B be x and y respectively, so the total wheat gives the equation (2x divided by 5) plus (3y divided by 10) equals 5, and the total rice gives (3x divided by 5) plus (7y divided by 10) equals 11. Multiplying both equations by 10 yields 4x plus 3y equals 50 and 6x plus 7y equals 110. Solving this system of equations by eliminating x gives 5y equals 70, so y is 14 kg, and substituting back gives 4x plus 42 equals 50, meaning x is 2 kg.

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