Math Problem!?

Question

In a math club of sixty members, each member either owns a computer or a chess set or both. One-half of those who own a computer also own a chess set. One third of those who own a chess set also own a computer. How many members own both?

Solution is 15

Answer 1

own Computer C
own Chess S
own Computer only Co
own Chess only So
own both C n S

1/2 C = C n S ==> C = 2(CnS)
1/3 S = C n S ==> S = 3(CnS)

Total = C + S - CnS
Total = Co + So + CnS

Total = C + S - CnS
Total = 2(CnS) + 3(CnS) - CnS
Total = 4(CnS)

CnS = 1/4 from Total
CnS = 1/4 (60)
CnS = 15

15 member own Both Computer and Chess