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?
A. 3
B. 6
C. 7
D. 1
Let X be the number of rare coins they had when they started collecting.
Miguel now has X + 5*38 rare coins.
Grace now has X + 3*24 rare coins.
We know that X + 5*38 = X + 3*24.
Combining like terms, we get 190 = 72 + X.
Subtracting 72 from both sides, we get 118 = X.
Therefore, the answer is A. 3.