6 m of soil containing 50% clay was mixed into 10 m of soil containing 10% clay. What is the clay content of the mixture?
How much salt should be added to 80 pounds of a 5 % salt solutio to make it a 24% salt solution
Thank you so much!
To find the clay content of the mixture in the first question, you need to calculate the total amount of clay in the two soil samples and then find the percentage of clay in the mixture.
1. Soil A: 6 m of soil containing 50% clay
To find the amount of clay in Soil A:
Amount of clay in Soil A = 6 m * 0.5 (50% as decimal) = 3 m
2. Soil B: 10 m of soil containing 10% clay
To find the amount of clay in Soil B:
Amount of clay in Soil B = 10 m * 0.1 (10% as decimal) = 1 m
3. Total amount of clay in the mixture:
Total amount of clay = Amount of clay in Soil A + Amount of clay in Soil B = 3 m + 1 m = 4 m
4. Total volume of the soil mixture:
Total volume of soil = Volume of Soil A + Volume of Soil B = 6 m + 10 m = 16 m
5. Clay content in the mixture:
Clay content = Total amount of clay / Total volume of soil mixture = 4 m / 16 m = 0.25 (25% as a decimal or 25% clay content in the mixture)
Therefore, the clay content of the mixture is 25%.
For the second question, to find the amount of salt that should be added to the 80 pounds of a 5% salt solution to make it a 24% salt solution, you can use the concept of mixtures.
Let's assume the amount of salt to be added is x pounds.
1. Initial salt content:
Initial salt in the 80 pounds of a 5% salt solution = 80 pounds * 0.05 (5% as decimal) = 4 pounds
2. Final salt content:
Final salt in the mixture = 80 pounds + x pounds
3. Using the concept of mixtures, we can set up the following equation:
(4 pounds + x pounds) / (80 pounds + x pounds) = 0.24 (24% as decimal)
4. Cross-multiplying and simplifying the equation:
4 pounds + x pounds = 0.24 * (80 pounds + x pounds)
4 + x = 0.24 * 80 + 0.24 * x
4 + x = 19.2 + 0.24x
5. Solving for x:
0.76x = 15.2
x = 15.2 / 0.76
x = 20 pounds
Therefore, 20 pounds of salt should be added to the 80 pounds of a 5% salt solution to make it a 24% salt solution.
You're welcome! If you have any more questions, feel free to ask.