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: 14

1 answer

To find the number of rare coins they had all together when they started collecting, we need to find the total number of coins Miguel and Grace have now and then subtract the number of coins they have currently from the total.

Miguel has been collecting 5 coins each week for a total of 5 * 7 = <<5*7=35>>35 coins.
He now has 38 coins, so when he started collecting he had 38 - 35 = <<38-35=3>>3 coins.

Likewise, Grace has been collecting 3 coins each week for a total of 3 * 8 = <<3*8=24>>24 coins.
She now has 24 coins, so when she started collecting she had 24 - 24 = <<24-24=0>>0 coins.

Together, when they started collecting, they had 3 + 0 = 3 coins.
Therefore, the answer is A: 3.