Question 101946
Let x=original number of apples in the basket

1st person gets (1/3)x
2nd person gets(1/4)x
3rd person gets(1/8)x
4th person gets (1/5)x
5th person gets ---10 apples
6th person gets-------1 apple

After the first four persons get their apples, we'll find out what fraction of the apples are left for the 5th and 6th persons and we are told that whatever that fraction is, will equal 11:

(1/3)x+(1/4)x+(1/8)x+(1/5)x=  Multiply each term by 120/120, the LCM:

(40/120)x+(30/120)x+(15/120)x+(24/120)x=(109/120)x

So, the apples that are left for the 5th & 6th persons equals:
(120/120)x-(109/120)x=(11/120)x  ---and this equals 11.
(11/120)x=11  multiply both sides by 120

11x=1320  divide both sides by 11


x=120--------------------------number of apples 

CK
(40/120)*120+(30/120)*120+(15/120)*120+(24/120)*120+11=120 or all the apples
40+30+15+24+11=120

109+11=120
120=120

Another way to work this problem is as follows:

(1/3)x+(1/4)x+(1/8)x+(1/5)x+11=x 

(109/120)x-x=-11
-(11/120)x=-11
-11x=-1320
x=120


Hope this helps---ptaylor