Question

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?

Answer 1

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

Answer: Bob has 249 coins