+414 Alice, Bernice, Celine, Devi had a total of 156 stamps. Alice lost 22 stamps and Bernice bought 16 stamps. If Devi had 3 times the number of stamps she originally had, then all of them would have an equal number of stamps. How many stamps did Celine have at first?
+129852 Alice, Bernice, Celine, Devi had a total of 156 stamps. Alice lost 22 stamps and Bernice bought 16 stamps. If Devi had 3 times the number of stamps she originally had, then all of them would have an equal number of stamps. How many stamps did Celine have at first?
Let w = Alice's original number of stamps, x = Bernice's original number of stamps, y = Celine's original number of stamps and z = Devi's original number of stamps
And we have this system :
w + x + y + z = 156 (1)
y = 3z (2)
w - 22 = 3z → w = 3z+ 22 (3)
x + 16 = 3z → x = 3z - 16 (2)
And substituting (2), (3) and (4) into (1), we have :
[3z + 22] + [ 3z - 16] + 3z + z = 156 simplify
10z + 6 = 156
10z = 150
z = 15
Celine had/has 3(15) = 45 stamps
Check
67 + 29 + 45 + 15 = 156
