Answer:
To solve this problem, we need to determine the amount of dry salt that needs to be added to the 150 kg of aqueous salt solution to increase its concentration from 15% to 40%.
Step 1: Calculate the initial amount of salt in the 150 kg solution:
Initial salt mass = 15% of 150 kg = 0.15 * 150 kg = 22.5 kg
Step 2: Calculate the final desired amount of salt in the solution:
Final salt mass = 40% of total mass (150 kg + added salt)
Final salt mass = 0.40 * (150 kg + added salt)
Step 3: Set up an equation based on the amount of salt:
Final salt mass = Initial salt mass + added salt mass
Substituting the values from Step 1 and Step 2, we have:
0.40 * (150 kg + added salt) = 22.5 kg + added salt
Step 4: Solve for the added salt:
0.40 * 150 kg + 0.40 * added salt = 22.5 kg + added salt
60 kg + 0.40 * added salt = 22.5 kg + added salt
Subtracting added salt from both sides:
60 kg = 22.5 kg + 0.60 * added salt
Subtracting 22.5 kg from both sides:
37.5 kg = 0.60 * added salt
Dividing both sides by 0.60:
added salt = 37.5 kg / 0.60 ≈ 62.5 kg
Therefore, approximately 62.5 kg of dry salt must be added to the 150 kg aqueous salt solution to increase its concentration from 15% to 40%.