Answer: i hope this step by step helps
Step-by-step explanation: To solve this problem, let's use the method of mixtures. We are given an initial solution containing 160 gallons and 12% salt. We need to find out how much pure water should be evaporated so that the remaining solution contains 20% salt.
Let's fill in the table:
| Original | Removed | New |
|------------------|---------|------|
| Amount of salt | | |
| Total solution | | |
The original amount of solution in gallons (a) is 160 gallons.
Next, let's calculate the amount of salt in the original solution. Since the original solution contains 12% salt, we can multiply the total solution by 0.12 to find the amount of salt:
Amount of salt = 0.12 * a
Now, we need to determine how much salt should be removed from the solution. The difference between the original and new salt amounts will give us the amount of salt removed:
Removed (salt) = Amount of salt (original) - Amount of salt (new)
The new solution needs to contain 20% salt. We can find the amount of salt in the new solution by multiplying the total solution (a - removed) by 0.2:
Amount of salt (new) = 0.2 * (a - removed)
Finally, we can calculate the amount of solution that needs to be removed by subtracting the new solution's amount of salt from the original solution's amount of salt and dividing it by the difference in salt concentration (0.12 - 0.2):
Removed (solution) = (Amount of salt (original) - Amount of salt (new)) / (0.12 - 0.2)
Now, we can fill in the table:
| Original | Removed | New |
|------------------|---------|--------------|
| Amount of salt | 0.08a | 0.2(a - r) |
| Total solution | r | a - r |
Please note that the values in the table may vary depending on the specific calculation. The steps described above will guide you in finding the appropriate values.
I hope this helps! Let me know if you have any further questions.