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?
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.
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
To solve this problem, we need to work backwards. We are given that after all the purchases, Shawn has $15 left. Let's find out how much money Shawn has after each purchase.
First, Shawn spends 1/6 of the remaining money on a candy bar. So, after this purchase, Shawn has 1 - 1/6 = 5/6 of the remaining money left.
Next, Shawn spends 1/4 of the remaining money on a DVD. So, after this purchase, Shawn has 5/6 - 1/4 = 5/12 of the remaining money left.
Then, Shawn spends 2/5 of the remaining money on games. So, after this purchase, Shawn has 5/12 - 2/5 = 1/12 of the remaining money left.
Finally, Shawn spends 1/3 of the remaining money on books. So, after this purchase, Shawn has 1/12 - 1/3 = -1/12 of the remaining money left.
Since we can't have negative money, we know that the remaining money after all the purchases is 0.
Now, we know that after the purchases, Shawn has $15 left, which represents the remaining money. Therefore, this remaining money is actually the original amount Shawn had. Therefore, Shawn originally had $15.