Nine wonderful students decided to buy their math teacher an expensive present, each contributing the same amount of money. Four other students found out about the plan and joined in, agreeing to pay their share of the present's cost. This resulted in a saving of $33.32 for each of the original 9 students. The cost of the gift, in dollars, was?

Answer 1

cost of gift ---- x
cost for each of the nine originals = x/9
cost per student with 13 paying = x/13

x/9 - x/13 = 33.32/9
times 117
13x - 9x = 3898.44
4x = 3898.44
x = 974.61

check:
original share = 974.61/9 = 108.29
new share = 974.61/13 = 74.97
saving per share = 33.32 , as required