Derek has 52.50 he can spend up to 1/3 of his money on school supplies. How much money can Derek save on school supplies?

Derek can spend up to 1/3 of his money, which is 52.50/3 = $<<52.50/3=17.50>>17.50 on school supplies.

Therefore, Derek can save 52.50 - 17.50 = $<<52.50-17.50=35>>35 on school supplies. Answer: \boxed{35}.