a store has a total of 108 full-time staff and part time staff. There are three times as many full-time staff as part time staff. How many of the staff are in each category?
PT + 3PT=108
4PT=108
PT=27 FT=108-27=81
27 part-time and 81 full-time
To solve this problem, we can set up a system of equations based on the given information. Let's use the following variables:
Let F represent the number of full-time staff.
Let P represent the number of part-time staff.
From the given information, we know the following:
F + P = 108 (Equation 1) - Total number of staff is 108.
F = 3P (Equation 2) - There are three times as many full-time staff as part-time staff.
Now we have a system of equations with two unknowns. We can solve them simultaneously to find the values of F and P.
We'll solve Equation 1 for F:
F = 108 - P.
Substituting this into Equation 2:
108 - P = 3P.
Combining like terms:
108 = 4P.
Divide both sides by 4:
27 = P.
So there are 27 part-time staff members.
Now substitute the value of P back into Equation 1 to find the number of full-time staff:
F + 27 = 108.
F = 108 - 27.
F = 81.
Therefore, there are 81 full-time staff members.
In summary, there are 81 full-time staff members and 27 part-time staff members in the store.