A company employs 4 times as many unskilled workers as it does skilled workers.
Unskilled workers earn $650 a week, and skilled workers earn $850 a week. The
weekly wage bill for these workers is $17 250. How many skilled and unskilled
workers are there?
Simultaneous equations
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To solve this problem, we can set up a system of simultaneous equations. Let's assign variables to the unknowns:
Let x be the number of skilled workers.
Let y be the number of unskilled workers.
We know that the company employs 4 times as many unskilled workers as skilled workers, so we can write the equation:
y = 4x (1)
We also know that unskilled workers earn $650 a week, skilled workers earn $850 a week, and the weekly wage bill is $17,250. We can write another equation based on this information:
650y + 850x = 17250 (2)
Now we have a system of two equations. We can solve this system by substitution or elimination to find the values of x and y.
Let's use substitution. We can substitute the value of y in equation (2) from equation (1) since we already know the relation between x and y:
650(4x) + 850x = 17250
Simplifying, we have:
2600x + 850x = 17250
Combining like terms:
3450x = 17250
Dividing both sides by 3450:
x = 5
Now we have the value of x. We can substitute this back into equation (1) to find y:
y = 4(5)
y = 20
So, there are 5 skilled workers and 20 unskilled workers in the company.