Question

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 friends liters should you mix to make 30 liters of 15% sodium?

Answer 1

To create a 15% sodium solution from 10% and 22% concentrations, you should mix 18 liters of the 10% sodium solution with 12 liters of the 22% sodium solution.

Step-by-step explanation:

To solve this problem, we can use a system of equations to express the total liters and the concentration of the sodium in the final solution. Let x be the liters of 10% sodium solution and y be the liters of 22% sodium solution. We are aiming for a 15% sodium solution with a total volume of 30 liters.

The first equation is for the total liters:

• x + y = 30

The second equation is for the sodium concentration:

• (0.10x + 0.22y) / 30 = 0.15

These equations can be rewritten as:

1. x + y = 30
2. 10x + 22y = 30 * 15

Solving the equations simultaneously, we find that:

• x = 18 liters (10% sodium solution)
• y = 12 liters (22% sodium solution)

Therefore, you should mix 18 liters of 10% sodium solution with 12 liters of 22% sodium solution to obtain 30 liters of a 15% sodium solution.

Answer 2

x liters of 10% + (30 - x) liters of 22% = 30 liters of 15%

Plugging in the numbers
x(10) + (30 - x)22 = 30(15)

Distribute
10x + 660 - 22x = 450

Combine like terms
-12x = -210

Divide both sides by -12
x = 17.5
30 - x = 12.5

17.5 liters of 10% + 12.5 liters of 22% = 30 liters of 15%