Andrew has seven fewer coins than casey. bob has three more than twice as many coins as andrew. altogether, they have 502 coins. how many coins does bob have?

Let C is the number of coins Casey has
Andrew has seven fewer coins than casey = C - 7
Bob has three more than twice as many coins as Andrew = 2(C-7) + 3
altogether, they have 502 coins = C + (C - 7) + 2(C-7) + 3 = 502

Now solve for C:
C + (C - 7) + 2(C-7) + 3 = 502
C + C - 7 + 2C  - 14 + 3 = 502
4C - 18 = 502
4C = 502 + 18
4C = 520
C =520/4
C = 130

So Casey has 130 coins
Andrew: C - 7 = 130 - 7 = 123
Bob: 2(C-7) + 3 = 2(130 - 7) + 3 = 2(123) + 3 = 246 + 3 = 249

Proof: 130 + 123 + 249 = 502

Bob has 249 coins