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Linear equations in two variables SAT question
Math · Algebra · Hard · Answer it here, explanation included.
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?
Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.
ExplanationShow
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 ,
, and
, 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
must be true. Multiplying 3 by 0.10 and distributing 0.15 to
yields
. Subtracting 0.15x and 0.30 from each side of the equation gives
. Dividing each side of the equation by 0.10 yields
. Note that 1.5 and 3/2 are examples of ways to enter a correct answer.
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