The average salary of a group of unskilled workers is 10000 and that o...
The average salary of a group of unskilled workers is 10,000 and that of a group of skilled workers is 15,000. If the combined salaries amount to 12,000, we can calculate the present age of the skilled workers as follows:
Step 1: Understand the problem
We are given the average salaries of unskilled and skilled workers, as well as the combined salary amount. We need to find the present age of the skilled workers.
Step 2: Set up the problem
Let's assume there are 'x' unskilled workers and 'y' skilled workers in the group. We can set up the following equations based on the given information:
1. (10,000 * x) + (15,000 * y) = 12,000 (combined salaries equation)
2. x + y = total number of workers in the group (unknown)
Step 3: Solve the equations
We have two equations and two unknowns, so we can solve them simultaneously. Let's solve for 'x' and 'y' using the method of substitution:
From equation 2, we can express 'x' in terms of 'y' as x = total number of workers - y.
Substituting this expression for 'x' in equation 1, we get:
(10,000 * (total number of workers - y)) + (15,000 * y) = 12,000.
Expanding the equation, we get:
10,000 * total number of workers - 10,000 * y + 15,000 * y = 12,000.
Combining like terms, we have:
10,000 * total number of workers + 5,000 * y = 12,000.
Step 4: Simplify and solve for 'y'
To isolate 'y', we can subtract 10,000 * total number of workers from both sides of the equation:
5,000 * y = 12,000 - 10,000 * total number of workers.
Dividing both sides of the equation by 5,000, we get:
y = (12,000 - 10,000 * total number of workers) / 5,000.
Step 5: Calculate the present age of skilled workers
Now that we have the value of 'y', we can substitute it back into equation 2 to find the present age of the skilled workers:
x + (12,000 - 10,000 * total number of workers) / 5,000 = total number of workers.
Simplifying the equation further, we get:
x = total number of workers - (12,000 - 10,000 * total number of workers) / 5,000.
This equation gives us the present age of the unskilled workers. To find the present age of the skilled workers, we subtract the age of the unskilled workers from the total number of workers:
Present age of skilled workers = total number of workers - present age of unskilled workers.
Step 6: Conclusion
By following these steps and solving the equations, we can determine the present age of the skilled workers.