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Algebra / Linear equations in two variables Difficulty: Hard

How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?

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Explanation

The correct answer is 1.5. The total amount, in liters, of a saline solution can be expressed as the liters of each type of saline solution multiplied by the percent concentration of the saline solution. This gives 3 times 0 point 1 0, x times 0 point 2 5, and open parenthesis, x plus 3, close parenthesis, times, open parenthesis, 0 point 1 5, close parenthesis, where x is the amount, in liters, of 25% saline solution and 10%, 15%, and 25% are represented as 0.10, 0.15, and 0.25, respectively. Thus, the equation 3 times 0 point 1 0, plus 0 point 2 5 x, equals, 0 point 1 5 times, open parenthesis, x plus 3, close parenthesis must be true. Multiplying 3 by 0.10 and distributing 0.15 to open parenthesis, x plus 3, close parenthesis yields 0 point 3 0, plus 0 point 2 5 x, equals, 0 point 1 5 x, plus 0 point 4 5. Subtracting 0.15x and 0.30 from each side of the equation gives 0 point 1 0 x, equals 0 point 1 5. Dividing each side of the equation by 0.10 yields x equals 1 point 5. Note that 1.5 and 3/2 are examples of ways to enter a correct answer.