QuestionAugust 25, 2025

How much water must be evaporated from 36 ounces of a 7% salt solution to make a 9% salt solution? To obtain a solution that is 9% salt. square ounce(s) of water must be evaporated. (Simplify your answer.)

How much water must be evaporated from 36 ounces of a 7% salt solution to make a 9% salt solution? To obtain a solution that is 9% salt. square ounce(s) of water must be evaporated. (Simplify your answer.)
How much water must be evaporated from 36 ounces of a 7% salt solution to make a 9% salt solution? To obtain a solution that is 9% salt. square ounce(s) of water must be evaporated. (Simplify your answer.)

Solution
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Answer

8 ounce(s) Explanation 1. Define Variables Let x be the amount of water to evaporate. The initial solution has 36 ounces with 7\% salt, so it contains 0.07 \times 36 = 2.52 ounces of salt. 2. Set Up Equation for Final Solution After evaporating x ounces of water, the new total weight is 36 - x ounces. We want this to be a 9\% salt solution: 0.09(36 - x) = 2.52. 3. Solve the Equation Solve 0.09(36 - x) = 2.52: - 0.09 \times 36 - 0.09x = 2.52 - 3.24 - 0.09x = 2.52 - 0.72 = 0.09x - x = \frac{0.72}{0.09} = 8

Explanation

1. Define Variables<br /> Let $x$ be the amount of water to evaporate. The initial solution has 36 ounces with $7\%$ salt, so it contains $0.07 \times 36 = 2.52$ ounces of salt.<br /><br />2. Set Up Equation for Final Solution<br /> After evaporating $x$ ounces of water, the new total weight is $36 - x$ ounces. We want this to be a $9\%$ salt solution: $0.09(36 - x) = 2.52$.<br /><br />3. Solve the Equation<br /> Solve $0.09(36 - x) = 2.52$:<br />- $0.09 \times 36 - 0.09x = 2.52$<br />- $3.24 - 0.09x = 2.52$<br />- $0.72 = 0.09x$<br />- $x = \frac{0.72}{0.09} = 8$
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