High School

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How many ounces of a 19% alcohol solution and a 29% alcohol solution must be combined to obtain 90 ounces of a 25% solution?

A. 27 oz of 19%, 63 oz of 29%
B. 36 oz of 19%, 54 oz of 29%
C. 45 oz of 19%, 45 oz of 29%
D. 54 oz of 19%, 36 oz of 29%

Answer :

Final answer:

To obtain 90 ounces of a 25% alcohol solution, a mixture of 54 ounces of a 19% alcohol solution and 36 ounces of a 29% alcohol solution is required. This is determined by solving a system of equations representing volume and alcohol concentration.

Explanation:

The student is asking how to mix two solutions of different alcohol concentrations to obtain a specific volume of a new solution with a desired alcohol concentration. To solve this, we use a system of equations based on the principle that the amount of alcohol in the final solution must be the result of the alcohol in the two original solutions.

Let x be the amount of 19% solution and y be the amount of 29% solution. The total volume is 90 ounces, so:

  • x + y = 90 (total volume equation)
  • 0.19x + 0.29y = 0.25×90 (alcohol content equation)

By solving the system of equations, we can find the values of x and y that satisfy both equations. After solving, we find that 54 oz of 19% and 36 oz of 29% will give us 90 ounces of a 25% alcohol solution. Therefore, the correct answer is option d.

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