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Nora and Renata had an equal number of polished stones at first. After Nora received 65 more stones and Renata lost 23 stones, Nora had three times as many stones as Renata. How many stones did they have altogether at first?

 Sep 16, 2021
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 Nora and Renata had an equal number of polished stones at first.     

 After Nora received 65 more stones and Renata lost 23 stones, Nora had three times as many stones as Renata.     

 How many stones did they have altogether at first?      

 

 N = Nora's original number of stones     

 R = Renata's original number of stones     

 

 N = R     

 (N + 65)  =  3 • (R – 23)     

 

 N = R so substitute it          (N + 65)  =  3 • (N – 23)     

                                               N + 65  =  3N – 69     

                                                   –2N  =  –134     

                                                       N  =  67    

 since N = R                                    R  =  67     

 

 check answer     

 

 does (67 + 65)  =  3 • (67 – 23) ?     

                  132  =  201 – 69     

                  132  =  132   True      

.     

 Nov 13, 2025

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