SOLUTION: apples are collected in a basket for six people. One-third, one-forth, one-eighth and one-fifth are given to four people, respectively. The fifth person gets ten apples with one

Question 101946: apples are collected in a basket for six people. One-third, one-forth, one-eighth and one-fifth are given to four people, respectively. The fifth person gets ten apples with one apple remaining for the sixth person. Find the original number of apples in the basket.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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

RELATED QUESTIONS
Apples are collected in a basket for 6 people. one third, one forth, one eighth, and one... (answered by scott8148)

Apples are collected in a basket for six people. One third, one fourth, one eighth, and... (answered by jorel1380)

Apples are collected in a basket for six people. One third,one fourth,one eighth, and one (answered by ptaylor)

Sharing fruit. Apples are collected in a basket for six people. One third, one fourth,... (answered by jorel1380)

Apples are collected in a basket for six people. One-third, one-fourth, one-eighth and... (answered by chitra)

Apples are collected in a basket for six people. One third, one fourth, one eighth, and... (answered by jrfrunner)

Please help me turn this into an equation, I am having a lot of trouble understanding it. (answered by Edwin McCravy)

1. Apples are collected in a basket for six people. One third, one fourth, one eight and... (answered by mananth)

Apples are collected in a basket for six people. One third, one fourth, one eight and one (answered by josmiceli)