When Clark was 7 years old he had 22 rare coins. Each year Clark added 15 coins to his collection. Assuming Clark does not sell or lose any coins, how old will Clark be when he has 577 coins?
Let C be the number of coins Clark has after Y years.
Clark starts with 22 coins, so C = 22.
Every year, Clark adds 15 coins to his collection, so for each additional year, C increases by 15: C = 22 + 15Y.
We need to find the value of Y when C = 577: 577 = 22 + 15Y
Subtracting 22 from both sides of the equation: 555 = 15Y.
Dividing both sides of the equation by 15: Y = 555 /15 = <<555/15=37>>37.
Therefore, Clark will be 7 + 37 = 44 years old when he has 577 coins. Answer: \boxed{44}.