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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
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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

 

 

cool cool cool

 Oct 3, 2015

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