Question

Shawn goes to store and spends 1/3 of money on books. He spends 2/5 of the remaining money on games. He spends 1/4 of the remaining money on a DVD. He spends 1/6 of remaining money on a candy bar. He has $15 left. How much money did Shawn have originally?

Answer 1

Does this sound right:

X = 2/3x * 3/5x * 3/4x * 5/6x + 15

X = 6/15 * 3/4 = 18/60 * 5/7 = 90/360 = 1/4
If 1/4 = $15 X would equal $60 original amount.

Answer 2

well, check your math. Starting with $60, that means
20 on books, leaving 40
16 on games, leaving 24
6 on DVD, leaving 18
3 on candy, leaving 15

We have a winner!

Your final step in concluding that if 1/4 of the money is $15 then the whole was $60 is correct.

But your original equation should have been

X * 2/3 * 3/5 * 3/4 * 5/6 = 15
X * 1/4 = 15
X = 60

Your equation as written would yield

x = 1/4 x^4 + 15
and that's just nonsense.

And even if you had written it as

x = (2/3 * 3/5 * 3/4 * 5/6)x + 15
that would have yielded
x = 1/4 x + 15
3/4 x = 15
x = 20