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# Help

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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?

Oct 3, 2015

#1
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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   Oct 3, 2015