Question 1184564


Nathan 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 Nathan have at first?
<pre>Let amount he started with be A
After spending {{{1/8}}}, he was left with {{{matrix(1,5, 7/8, of, A, "=", 7A/8)}}}
After spending {{{3/4}}} of remainder on shoes, he had {{{matrix(1,5, 1/4, of, 7A/8, "=", 7A/32)}}} remaining
After receiving $715 from his parents, he then had: {{{7A/32 + 715}}}
With {{{matrix(1,3, Remainder/matrix(1,2, Initial, amount), "=", 9/4)}}}, we finally have: {{{matrix(3,3, (7A/32 + 715)/A, "=", 9/4, 4(7A/32 + 715), "=", 9A, 7A/8 + "2,860", "=", 9A)}}}
7A + 8(2,860) = 72A ------ Multiplying by LCD, 8
     8(2,860) = 72A - 7A
     8(2,860) = 65A
   {{{highlight_green(matrix(2,3, 8("2,860")/65, "=", A, 8(44), "=", A))}}}
Initial amount he had: <font color = red><font size = 5><b>$352</font></font></b>