Question

system of equations You and your friend are making 30 liters of sodium water. You have liters of 10% sodium and your friend has liters of 22% sodium. How many of your liters and how many of your friend's liters should you mix to make 30 liters of 15% sodium

Answer 1

To mix 10% and 22% sodium solutions to get 30 liters of a 15% sodium solution, you need to set up a system of equations and solve for the quantities of each solution required.

Step-by-step explanation:

To solve the problem involving a system of equations for mixing solutions with different concentrations, we need to find out how many liters of 10% sodium solution and 22% sodium solution to mix to make 30 liters of 15% sodium water solution. Let the amount of the 10% solution be x liters and the amount of the 22% solution be y liters.

Based on the given information, we have two equations:

1. x + y = 30 (The total volume of the solutions must add up to 30 liters.)
2. 0.10x + 0.22y = 0.15 × 30 (The total amount of sodium in the mixed solution must be 15% of 30 liters.)

By solving these equations simultaneously, we find the values of x and y that will give us the right proportions of each solution to achieve the desired concentration.