We need two equations to solve this problem.
1. we know that x, the volume of 25% acid plus y, the volume of 40% acid will equal 144L. Algebraically, x + y = 144L
when we solve this equation for x, we get x = 144L - y
2. we know that C1V1 + C2V3 = C3V3 where C = Concentration, and V = Volume. Since we know the concentrations, we can write 0.25x + 0.40y = 0.25 144L, which becomes 0.25x + 0.4y = 38.88L
3. we substitute the value from equation 1 into the second equation, and we get 0.25(144L - y) + 0.4y = 38.88L
4. expanding our equation, we get 36L - 0.25y + 0.4y = 38.88L
5. solving for y, we get y = 19.2L. Thus, x = 144L - 19.2L = 124.8L
We can prove the solution by multiplying the concentration by the volumes, and we get (0.25 • 124.8L) + (0.4 • 19.2L) = 0.27 • 144L, and we get 31.2L + 7.7L = 38.9L
