Question how-ma

1.2 Linear Equations in One Variable - Word problems → single variable
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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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How many liters of a 25% saline solution must be added to 3 liters of a

Hard-difficulty · SAT Math · Linear Equations in One Variable — Word problems → single variable. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer 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.