HE THEN GIVES HIS SISTER 5/6 OF THE REMAINDER AND HAS 80 STAMPS LEFT. HOW MANY STAMPS DID GOMEZ HAVE AT FIRST ?

Question

GOMEZ COLLECTS STAMPS AS A HOBBY. HE GIVES HIS COUSIN 1/3 OF HIS STAMP COLLECTION. HE THEN GIVES HIS SISTER 5/6 OF THE REMAINDER AND HAS 80 STAMPS LEFT. HOW MANY STAMPS DID GOMEZ HAVE AT FIRST ?

Answer 1

Gomez has a total of S stamps
 
He gives to his cousin C stamps C = 1/3S
 
He gives his sister T stamps. 5/6 of what is left T = 5/6 (S - 1/3S)
 
He has 80 stamps left 80 = 1/6*(S - 1/3S) ==> S = 720
 
720*(1/3) = 240,
 
(720 -240)*5/6 = 400
 
400 + 240 + 80 = 720