Multiple choice

Four jars, P, Q, R, and S, contain mixtures of olive oil and vinegar in the ratios of 2 : 3, 5 : 7, 4 : 9, and 3 : 4, respectively. The capacities of the jars are in the ratio of 5 : 12 : 13 : 7. If the contents of all four jars are combined, what is the ratio of olive oil to vinegar in the resulting mixture?

  1. 7 : 17

  2. 4 : 9

  3. 14 : 23

  4. 14 : 27

  5. 17 : 27
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C Correct answer
Explanation

Total ratio = (Sum of olive oil) / (Sum of vinegar). Olive oil = 5*(2/5) + 12*(5/12) + 13*(4/13) + 7*(3/7) = 2 + 5 + 4 + 3 = 14. Vinegar = 5*(3/5) + 12*(7/12) + 13*(9/13) + 7*(4/7) = 3 + 7 + 9 + 4 = 23. Ratio = 14:23.

AI explanation

Let the capacities of jars P, Q, R, and S be 5x, 12x, 13x, and 7x. The total olive oil is calculated as (2/5 of 5x) plus (5/12 of 12x) plus (4/13 of 13x) plus (3/7 of 7x), which equals 2x plus 5x plus 4x plus 3x, totaling 14x. The total vinegar is found by subtracting the oil from the total capacity, so (5x minus 2x) plus (12x minus 5x) plus (13x minus 4x) plus (7x minus 3x) equals 23x. The final ratio of olive oil to vinegar is 14x to 23x, or 14 to 23.

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