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# algebra

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Gary, Mary, and Rory have the same number of candies. If Gary gives Mary half of all his candies, then Mary gives Rory half of all the candies she has at the moment, and then Rory gives Gary half of all the candies he (Rory) has at the moment, Gary would have 12 more candies than he had originally. How many candies do Gary, Mary, and Rory have altogether?

Mar 29, 2021

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Let  Gary, Mary  and  Rory  start out  with  N  candles each

Gary  gives  Mary  1/2 of his  candles

Mary  has   ( N + N /2)  =  (3/2)N  candles

Gary has N/2  candles

Mary gives Rory  half of  her candles

Mary  has (3/4)N candles

Rory  has (N + (3/4)N)  =  (7/4)N candles

Rory gives  Gary half of his  candles

Rory  has (7/8) candles

Gary  has  (N /2  + (7/8)N)  =  (11/8)N  candles

And now,  from Gary's point of  view, he started with

(11/8)N  =  N  + 12

(11/8)N - N  =12

(3/8)N =  12

N = 12 ( 8/3)  =      96 / 3  =  32  candles

They  have  3(32)  =  96 total candles

Mar 29, 2021
edited by CPhill  Mar 29, 2021