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how many gallons of a 30% antifreeze solution and a 15% antifreeze solution must be mixed to obtain 30 gal of a 22% antifreeze solution? round to the nearest gallon, if necessary.

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Final answer:

To achieve a 30 gallon mix of a 22% antifreeze solution, you would need to mix approximately 14 gallons of a 30% antifreeze solution and 16 gallons of a 15% antifreeze solution.

Step-by-step explanation:

This is a problem of mathematics, specifically dealing with proportions and percentages. You are asked how many gallons of a 30% antifreeze solution and a 15% antifreeze solution must be mixed to obtain 30 gal of a 22% antifreeze solution.

Let's denote the amount of the 30% antifreeze solution as X and the amount of the 15% antifreeze solution as Y. We need to solve the following system of equations:

1. X + Y = 30 (since the total amount of solution is 30 gallons)

2. 0.30X + 0.15Y = 0.22 * 30 (assuming that the percentages refer to the volume of the antifreeze in each solution)

When we solve this system of equations, we find that X (the 30% solution) should be approximately 14 gallons and Y (the 15% solution) should be approximately 16 gallons. Rounded to the nearest gallon, we need 14 gallons of the 30% solution and 16 gallons of the 15% solution, respectively.

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