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Tracy had a bag of candies, and none of the candies could be broken into pieces. She ate 1/3 of them and then gave 1/4 of what remained to her friend Rachel. Tracy and her mom then each ate 15 candies from what Tracy had left. Finally, Tracy’s brother took somewhere from one to five candies, leaving Tracy with three candies. How many candies did Tracy have at the start?

 May 23, 2020
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x = original number of candies

 

ate 1/3     means    2/3 x remains

 

gave away 1/4    means    3/4 * 2/3 x  reamins

 

ate 30        3/4 * 2/3 x - 30

 

Brat Brother took 1 to 5      so     3/4 * 2/3 x -30   -  (1 to 5) = 3

                                                     6/12 x  -  30     - 1to5 = 3     

                                                     6/12x - 1to5 = 33

                                                    

 

        6/12 x = 33    means x = 66        since BratBro took 1- 5 

 

6/12 (68) -1 =33

6/12 (70) - 2

6/12 (72) - 3     This is the only one that results in whole candies after 1/3 removed and 1/4 removed        72

6/12(74) -4

6/12(76) - 5

 May 23, 2020
edited by ElectricPavlov  May 23, 2020

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