Final answer:
The calculation determines the amounts of 15% and 5% alcohol solution needed to create a 6% solution. After forming an equation and solving for variables representing each type of solution, the results do not match any given options, suggesting an error in the question or insufficient information.
Step-by-step explanation:
The question asks us to determine how many gallons of 15% alcohol and 5% alcohol should be mixed to obtain x gallons of 6% alcohol. To solve this, we can use the concept of weight averages or alcohol content balancing. The total alcohol content in the final mixture must equal the sum of the alcohol content from each part of the 15% and 5% solutions. We represent the amount of 15% alcohol solution as y gallons and the amount of 5% alcohol solution as (x-y) gallons, where x is the total gallons of the final 6% alcohol solution.
Setting up the equation gives us: 0.15y + 0.05(x-y) = 0.06x. Solving for y will give us the quantity of 15% alcohol solution, and the quantity of 5% alcohol solution would be x-y. However, the actual values of y and x-y are not provided by the options a, b, c, or d, meaning we need to solve for the relationship between them to match one of the given options by simplifying the equation:
- 0.15y + 0.05x - 0.05y = 0.06x
- 0.10y = 0.01x
- y = 0.1x
The quantity of the 5% alcohol solution would then be x - 0.1x = 0.9x, which is not represented in any of the provided options either. Therefore, based on the given information, we are unable to select a correct matching pair from the options provided as none of them represents the proper ratio derived from solving the equation. This indicates either a mistake in the question or a lack of enough information to match the available options.