Multiple choice

A chemist has two solutions of alcohol and water. Solution A contains alcohol and water in the ratio 2 : 5, while Solution B contains alcohol and water in the ratio 5 : 8. The chemist decides to mix Solutions A and B in such a way that the resulting mixture has an alcohol-to-water ratio of 13 : 25. If the chemist needs to prepare 114 litres of the resulting mixture, how many litres of each solution should be mixed?

  1. 36 litres of Solution A and 78 litres of Solution B

  2. 49 litres of Solution A and 65 litres of Solution B

  3. 65 litres of Solution A and 49 litres of Solution B

  4. 66 litres of Solution A and 68 litres of Solution B

  5. a
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B Correct answer
Explanation

Let x be the amount of Solution A and y be the amount of Solution B. x + y = 114. Alcohol in A = 2/7, in B = 5/13. Mixture ratio 13:25 means alcohol is 13/38. (2/7)x + (5/13)y = (13/38) * 114 = 39. Solving the system: x + y = 114 => y = 114 - x. (2/7)x + (5/13)(114 - x) = 39. Multiply by 91: 26x + 35(114 - x) = 3549. 26x + 3990 - 35x = 3549. -9x = -441. x = 49. y = 114 - 49 = 65.

AI explanation

Using the values directly, Solution A has a total of 7 parts and Solution B has a total of 13 parts. The ratio of the quantity of Solution A to the total mixture for the given options would be A_quantity / 114. For the proportions to mathematically yield an exact 13:25 ratio, the parts must perfectly divide the 114 litres. Evaluating the options, 49 litres of Solution A and 65 litres of Solution B fulfills the required conditions.

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