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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?

MaiaMitchell  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

CPhill  Oct 3, 2015

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