Question

a chemist mixed x liters of a 4% saline solution with y liters of a 9% saline solution to produce a 7% saline solution. which equation best represents this situation? (assume the volumes of the solutions are additive.)
(a) 0.04x + 0.09y = 7(x + y)
(b) 0.04x + 0.09y = 0.07(x + y)
(c) 0.4x + 0.9y = 7(x + y)
(d) 0.4x + 0.9y = 0.7(x + y)

Explanation:

Step1: Calculate salt amount in each solution

The amount of salt in the 4% saline solution is $0.04x$ (since 4% = 0.04), and the amount of salt in the 9% saline solution is $0.09y$ (since 9% = 0.09).

Step2: Calculate salt amount in final solution

The total volume of the final solution is $x + y$ liters, and it is a 7% saline solution. So the amount of salt in the final solution is $0.07(x + y)$ (since 7% = 0.07).

Step3: Set up equation

Since the total salt before mixing equals the total salt after mixing, we have the equation $0.04x+0.09y = 0.07(x + y)$.

Answer:

B. $0.04x + 0.09y = 0.07(x + y)$