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Bmat help!

Can anyone help with this question, please?
In an experiment concerning radioactive decay the count rate of radiation 5cm from source X was measured at 140 counts per min. 12 mins later with the detector at the same position the count rate was measured at 35 counts per min. Background radiation was measured at 20 counts per minute. Clculate the half life of source X?
A) 1 min
B)2 mins
C)3 mins
D) 4 mins
E)5 mins

I got d) 4

heres my working but it might be wrong:

radiation =140- background radiation
=120

half life
0- 120
1- 60
2- 30
3- 15

radiation left= 35-background radiation = 15

15 left after 3 half lives
12/3= 4

each half life is 4 mins