Question

In the problem of mixing a 40% saline solution with a 60% saline solution to create a 44% solution, which of the following equations represents the situation?

a) x + y = 100 and 0.40x + 0.60y = 0.44(100)
b) x - y = 100 and 0.40x + 0.60y = 0.44(100)
c) x + y = 44 and 0.40x + 0.60y = 100
d) x + y = 44 and 0.44x + 0.60y = 100

Answer 1

The correct equations that represent the situation of mixing a 40% saline solution with a 60% saline solution to create a 44% saline solution are x + y = 100 and 0.40x + 0.60y = 0.44(100), which corresponds to option (a).

Step-by-step explanation:

To solve the problem of mixing a 40% saline solution with a 60% saline solution to create a 44% saline solution, we need to set up a system of equations. Let x represent the amount of 40% saline solution and y represent the amount of 60% saline solution. The total mixture is to be a 44% saline solution. The two equations representing this situation will account for both the total volume of the solution and the concentration of salt in the solution.

The first equation should represent the total volume, assuming we want 100 units of the new solution. This is expressed as x + y = 100. The second equation represents the total amount of salt which comes from 40% of x and 60% of y being equal to 44% of the total solution, or 0.40x + 0.60y = 0.44(100). So, the correct representation of the situation is given by option (a).