Multiple choice

Sarah, an enthusiastic chef, had to prepare a special marinade for her signature dish. In her kitchen, she had two containers labelled X and Y. Container X contained a mixture of vinegar and water in the ratio of 3 : 2, while Container Y had a solution of vinegar and water in the ratio of 5 : 8. To create the perfect blend for her marinade, Sarah needed to combine the contents of both containers. In what ratio should Sarah mix the solutions from Container X and Container Y to achieve a final mixture with a vinegar-to-water ratio of 7 : 10?

  1. 1 : 2

  2. 26 : 85

  3. 15 : 104

  4. 85 : 414

  5. 5 : 24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Use alligation. Container X: Vinegar = 3/5. Container Y: Vinegar = 5/13. Target: 7/17. (5/13 - 7/17) / (7/17 - 3/5) = ((85-91)/221) / ((35-51)/85) = (-6/221) / (-16/85) = (6/221) * (85/16) = (3/221) * (85/8) = (3*5) / (13*8) = 15/104.

AI explanation

The proportion of vinegar in container X is 3/5, in Y is 5/13, and in the desired mixture is 7/17. Using the rule of alligation, the ratio of X to Y is the difference between the desired mixture and Y divided by the difference between X and the desired mixture. This gives (7/17 - 5/13) / (3/5 - 7/17), which simplifies to (91 - 85)/221 divided by (51 - 35)/85, resulting in 6/221 * 85/16. This evaluates to 15/104.

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