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At the big glue stick party, Rob gives Sydney and Koreb as many glue sticks as each already has. Then Sydney gives Rob and Koreb as many glue sticks as each of them then has. Finally, Koreb gives Sydney and Rob as many glue sticks as each has. If, at the end of this avalanch of generosity, each person has sixteen glue sticks, how many glue sticks did each one have at the beginning?

 Jan 15, 2021
 #1
avatar+392 
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Hi mzhu23!

 

Chart

Let's make a chart where r is the number Rob has, s is the number of glue sticks Sydney has, and k is the number of glue sticks Koreb has at the beginning. 

 

Rob    Sydney    Koreb

r         s               k                 # Sydney gives Rob and Koreb as many glue sticks as each of them then has

2r       s - r - k      2k               # Koreb gives Sydney and Rob as many glue sticks as each has

4r       2(r - s - k)  3k - s - 2r

 

What do we know?

So from the graph what do we know. 

We know that: 

r + s + k = 48

4r = 16

2(s - r - k) = 16

3k - s - 2r = 16

 

Solving r

4r = 16

r = 4

 

Plugging r in past equations

4 + s + k = 48

s + k = 44 # New equation

2(s - r - k) = 16

s - r - k = 8

s - 4 - k = 8

s - k = 12 # New equation

3k - s - 2(4) = 16

3k - s = 24

 

Finding s and k

Two important equations from above are... s + k = 44 and s - k = 12. 

So, if we add them together, 2s = 56. 

s = 27. 

That would make k 15 (27 - 15 = 12)

 

Answer

Rob had 4 gluesticks. 

Sydney had 27 gluesticks. 

Koreb had 15 gluesticks. 

 

I hope this helped. :))))

=^._.^=

 Jan 15, 2021
 #2
avatar+14 
0

Hi catmg,

 

Thanks a lot! However the question says that Rob also gives Sydney and Koreb as many glue sticks as each already has, so your answer was incorrect. That's okay though, because your answer helped me understand how to do it, so I think I can solve it by myself now. Thanks! 

mzhu23  Jan 17, 2021

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