Problem Solving

can somebody help?

One night 18 percent of the female officers on a police force were on duty. If 180 officers were on duty that night and half of these were female officers, how many female officers were on the police force?

(a) 90
(b) 180
(c) 270
(d) 500
(e) 1000

Do I have to use the backsolving-methode? I tried but...

thanks a lot!

0.18(x) = 90
x = 500
IMO-D

Why do you want to use backsolving?


180 officers were on duty: half male half female:

so there were 90 female police officers on duty.

the question stem also says that 18% of the female force was on duty.

so (18/100)*x = 90

x = 500 = entire female police force.

If half of the officers on duty were female then total number of female officers = (90/ 18)*100 = 500