Peter had some money. He spent 1/8 of it on a T-shirt and 3/4 of the remainder on a pair of shoes. After that, his parents gave him $715. The ratio of the total amount of money he had left at the end to the amount of money he had at first was 9:4. How much did Peter have at first?

Answer 1

Let X be the amount of money Peter had at first.
Peter spent X/8 on a T-shirt.
Peter had X - X/8 = 7/8*X left.
Peter spent 3/4 * (7/8*X) = 21/32 * X on shoes.
Peter had 7/8*X - 21/32*X = 9/32*X left.
9/32*X / X = 9/32 = (9/4) / (32/1) = 9/4 * 1/32 = 9/128
So 9/128*X = 715 and X = 128/9 * 715 = 10240. Answer: \boxed{10240}.