A hospital has a 4%-saline solution and an 12%-saline solution on hand. How much of each should be used to prepare 640 cm ³ of 7%-saline solution? A) 240 cm ³ of a 12%-saline solution, 400 cm ³ of a 4%-saline solution. B) 220 cm ³ of a 12%-saline solution, 420 cm ³ of a 4%-saline solution. C) 400 cm ³ of a 12%-saline solution, 240 cm ³ of a 4%-saline solution. D) 340 cm ³ of a 12%-saline solution, 300 cm ³ of a 4%-saline solution. E) 440 cm ³ of a 12%-saline solution, 200 cm ³ of a 4%-saline solution.

Question

Quizplus · Accepted Answer

To prepare a 7%-saline solution from 4% and 12% solutions, we can use the method of weighted averages. Let $x$ be the amount of 12% solution and $640 - x$ be the amount of 4% solution. The equation to represent the mixture is $0.12x + 0.04(640 - x) = 0.07 \times 640$. Solving this equation gives $x = 240$, meaning 240 cm³ of the 12% solution and $640 - 240 = 400$ cm³ of the 4% solution are needed.

A Hospital Has a 4%-Saline Solution and an 12%-Saline Solution