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 he 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
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Let's assume that both Miguel and Grace started collecting rare coins x weeks ago.
Miguel has been collecting 5 coins each week, so after x weeks, he has collected 5x coins.
Grace has been collecting 3 coins each week, so after x weeks, she has collected 3x coins.
At the present time, Miguel has 38 coins and Grace has 24 coins.
Therefore, we can set up the equation:
5x = 38
3x = 24
Solving these equations, we find that x = 7.6
Since we cannot have a fraction of a week, we can round it down to 7 weeks.
So, Miguel and Grace started collecting rare coins 7 weeks ago.
To find the total number of rare coins they had when they started collecting, we can add their individual collections:
Miguel: 5 coins/week x 7 weeks = 35 coins
Grace: 3 coins/week x 7 weeks = 21 coins
Therefore, when they started collecting, Miguel and Grace had a total of 35 + 21 = 56 rare coins.