VJesus12 wrote: ↑Sun Aug 15, 2021 8:09 am
From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4. From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3. If there were 100 employees at the company in 2006, how many employees were there at the company in 2000?
A. 200
B. 120
C. 100
D. 75
E. 60
Answer:
B
Source: Official Guide
From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4
Let x = the number of employees in 2000
So, the number of employees in 2003 = x + (1/4)x
=
(5/4)x
From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3
(5/4)x = the number of employees in 2003
So, the number of employees in 2006 =
(5/4)x - (1/3)(
(5/4)x
=
(5/4)x - (5/12)x
=
(15/12)x - (5/12)x
= (10/12)x
=
(5/6)x
If there were 100 employees at the company in 2006, how many employees were there at the company in 2000 ?
We can write:
(5/6)x = 100
Multiply both sides by 6 to get; 5x = 600
Solve: x = 600/5 = 120
Answer: B
Cheers,
Brent
