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?

MaiaMitchell
Oct 3, 2015

#1**+5 **

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

CPhill
Oct 3, 2015