Suppose that x liters of 40% acid solution are mixed with y liters of a 43% solution to obtain 100 L of a 41% solution. One equation in a system for solving this problem is x + y = 100. What is the other equation?
.40x + .43y = .41(100)
To find the other equation in the system, we need to consider the amount of acid in the mixture.
Let's start by calculating the amount of acid in x liters of the 40% solution. The concentration of the acid is given as 40%, which means that 40% of x liters is acid. This can be expressed as 0.40x.
Similarly, the amount of acid in y liters of the 43% solution is 0.43y.
Since we are mixing these two solutions to obtain 100 liters of a 41% solution, the total amount of acid in the mixture should be 41% of 100 liters, which is 0.41 * 100 = 41.
Therefore, the second equation in the system is: 0.40x + 0.43y = 41.
So, the complete system of equations is:
1) x + y = 100
2) 0.40x + 0.43y = 41