miguel and grace started collecting rare coins at the same time , back then they had the same number of rare coins , miguel has been collecting 5 coins each week and how now has 38 coins grace has been collecting 3 coins each week and she now has 24 coins how many rare coins did they have all together when they started collecting
If Miguel has been collecting 5 coins each week and now has 38 coins, then he has been collecting for a total of 38/5 = <<38/5=7.6>>7.6 weeks.
Since the number of weeks must be whole numbers, Miguel has been collecting rare coins for 7 weeks.
If Grace has been collecting 3 coins each week and now has 24 coins, then she has been collecting for a total of 24/3 = <<24/3=8>>8 weeks.
Since the number of weeks must be whole numbers, Grace has been collecting rare coins for 8 weeks.
Since Miguel and Grace started collecting at the same time, and they have been collecting for 7 weeks and 8 weeks respectively, then the total number of rare coins they had together when they started collecting is 7+8 = <<7+8=15>>15 rare coins. Answer: \boxed{15}.