Multiple choice

If x beakers of 100 ml containing 1 : 4 acid-water solution are mixed with y beakers of 200 ml containing 3 : 17 acid-water solution, then the ratio of acid to water in the resulting mixture becomes 19 : 91. Find x : y.

  1. 5 : 3

  2. 3 : 5

  3. 7 : 13

  4. 13 : 7
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AI explanation

The acid in the first type of beaker is 1 over 5 of 100 ml, equaling 20 ml, while the acid in the second type is 3 over 20 of 200 ml, equaling 30 ml. The desired acid to total mixture ratio is 19 over 110, meaning the acid in one combined unit of x and y is (20x plus 30y) divided by (100x plus 200y). Equating this to 19 over 110 gives 2200x plus 3300y equals 1900x plus 3800y, which simplifies to 300x equals 500y, yielding the ratio 5 to 3.

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