Final answer:
By applying the conservation of mass and setting up an equation based on the salt concentrations of the solutions involved, we calculate that 10 liters of 10% saltwater needs to be added to 5 liters of 25% saltwater to achieve a final concentration of 15%.
Step-by-step explanation:
To solve the problem of mixing solutions with different salt concentrations, we can use the concept of the conservation of mass. Specifically, the total mass of salt in the final solution must be equal to the sum of the mass of salt in the individual solutions mixed together.
The mass of salt in the 25% solution is 5 liters times 25%, which gives us 1.25 liters of salt. If we let x be the number of liters of 10% salt water added, then the mass of salt from this part would be x liters times 10%, which gives us 0.1x liters of salt. The final solution volume is 5 liters plus x liters, and it should have a 15% salt concentration. The mass of salt in the final solution should therefore be (5 + x) liters times 15%, which yields 0.15(5 + x) liters of salt.
Setting up the equation:
1.25 + 0.1x = 0.15(5 + x)
Solving for x gives:
1.25 + 0.1x = 0.75 + 0.15x
0.05x = 0.5
x = 10 liters
Thus, the answer is 10 liters.