Sheik had some $2, $5 and $10 notes. The ratio of the number of $2 notes to the number of $5 notes to the number of $10 notes was 1: 3: 5. After spending all his $10 notes and 5/6 of his $5 notes, he had $783 left. How much money did he have at first?
T=2-dollar notes, F=5-dollar notes, N=10-dollar notes
1/3 = T / F............................(1)
3/5 = F / N...........................(2)
2T + 1/6[5F] = 783..............(3), solve for T, F, N
T = 174 - number of 2-dollar notes at first
F = 522 - number of 5-dollar notes at first
N=870 - number of 10-dollar notes at first.
$174 + $522 + $870 = $1,566.00 - Total amount he had at first.