The unit qt is short for the mass unit quart. To solve this, we formulate two equations. The first is the overall mass balance, and the second is the component mass balance. Let x be mass of 30% salt solution and y be the mass of 70% salt solution.
Overall mass balance: x + y = 20
Component Mass Balance: 0.3x + 0.7y = 20(0.4)
Rearranging the first equation, x = 20 - y. Substitute this to the second equation:
0.3(20 - y) + 0.7y = 20(0.4)
Solving for y,
y = 5 qt
Solving for x,
x = 20 - 5 = 15 qt
Therefore, you need 15 qt of 30% salt solution, and 5 qt of 70% salt solution.
