Question

Dan spent 1/5 of his money and an additional $4 on a CD. He then spent 1/3 of his
remaining money and an additional $8 on some comics. Given that he was left with $24
how much money did he have at first?

Answer 1

Had d
after Cd he had d - d/5 - 4 = 4d/5-4
after comics he had (4d/5-4) - (4d/5-4)/3 - 8
(4d/5-4) - (4d/5-4)/3 - 8 =24

(4d/5-4) - (4d/5-4)/3 =32
3(4d/5-4) - (4d/5-4) = 96
2 d/5 - 8 = 96
2 d/5 = 104
d/5 = 52
d = 260

Answer 2

start with x
spends x/5 + 4
amount left = x - (x/5 + 4) = 4x/5 - 4
spends 1/3 of that +8
= (1/3)(4x/5 - 4) + 8
= 4x/15 - 4/3 + 8
= 4x/15 + 20/3

4x/5 - 4 - (4x/15 + 20/3) = 24
times 15
12x - 60 - 4x - 100 = 360
8x = 520
x = 65

check:
amount spent at first = (1/5)(65) + 4 = 17
amount left = 48
spends 1/3 of that +8 = 24
amount left = 48-24 = 24