How do I solve this fraction?

Question

1/3 of employees work in the clerical department, 1/4 of the employees work in the fiscal department, and there are 2100 employees who work as caseworkers, how many employees are there total?

Answer 1

1/3=4/12 clerical
1/4=3/12 fiscal
leaves 5/12 as caseworkers

5/12 =2100/x
x equals total employees
cross multiply to get:
5x=25200
x=5040
There are therefore 5040 employees!!
That's my final answer!!
Have a great day!!

Answer 2

If 1/3 of employees work in clerical department and 1/4 of employees work in the fiscal department that means that 5/12 works as caseworkers as 1/3+1/4=7/12
You then divide 2100 by 5 to get 1 unit....2100/5=420
then multiply it by 12=5040...this is the total number of employees in total

Answer 3

The caseworkers =(1-1/3-1/4)=5/12 of the workforce as 4/12 (1/3) are clerical and 3/12 (1/4) are fiscal.
So total employees will be 2100x12/5=5040

Answer 4

There are 5040 employees total.

1/3 clerical is 4/12
1/4 fiscal is 3/12
Those 2 departments equal 7/12
which leaves 5/12 for the 2100 caseworkers
2100/5=420 per 1/12

1/3 of 5040=1680
1/4 of 5040=1260
1680+1260+2100=5040

I know this is the long way around to the answer. (I can't remember how to do the algebraic notation.)

edit: I see I took so long to write this that a few others answered correctly as well! And made the proper algebraic formulas! Nicely done all!

Answer 5

If we presume that 100% of the workers are employed as caseworkers / clerical / fiscal, then the solution is straightforward.

The caseworkers must represent 5/12 of the workforce as 4/12 (1/3) are clerical and 3/12 (1/4) are fiscal. Therefore total employees will be 5040 ie (2100/5)x12

Answer 6

I will make an assumption here... that the employees of the clerical and the fiscal department together with the caseworkers mae the total. Therefore you have an equation with one single variable:

1/3*X+1/4*X=X-2100, where X is the total number of the employees.

multiple everything by 12 =>

12*1/3*X+12*1/4*X=12X -25200 =>
=> 4X+3X=12X -25200 =>
=> 5X = 25200 =>
=> X = 5040

I think the assumption is correct, but I might be wrong

Answer 7

Let total number of employees = x
x/3 + x/4 +2100 = x
4x + 3x + 25200 = 12x
5x = 25200
x = 5040
There are 5040 employees in total.

Answer 8

assuming that there are 3 depts.
(don't round digits)
1/3 = 0.33333

1/4 = 0.25

0.3333334 + 0.25 + y = 1

y = 0.42 (leftover percentage)
2100 = 0.42x

x = 2100 / 0.42

x = 5040

also, 1/3 + 1/4 = 7/12

1 - 7/12 =5/12 (the missing percentage)

2100 = 5/12 x

x = (2100 /5 ) x 12

Answer 9

Ermm how many departments are there in total? And what is the caseworkers' categorized departments??

The rest is easy.. well kinda. It's just a little too vague to answer now.