Suppose figurine A costs $7 and figurine B costs $10. You have n dollars and want to spend all of your money on figurines. Prove by mathematical induction that there are non-negative integers x and y such that, by purchasing x copies of figurine A and y copies of figurine B, all n dollars will be spent for any n 54. Hint: unlike a typical induction problem, there are many base cases here, and the first base case is n = 54, not n = 0.