# Solving for the original amount after spending x amount per things.

Problem: Midoriya goes to a bake shop to buy some pastries for resale at Book Latte. He spends half his money for Revel Bars, and one-third of what remains for Triple Chocolate Brownies. He spends 150 for other pastries and still has 200 left from the amount he originally had. How much money did he have at the start?

Attempt 1: Making x = the original amount. $x - \frac{1}{2}x - \frac{1}{3}x -150 = 200.$ Solving for x, the result is 2100 which is wrong. :(

Attempt 2: $x - \frac{1}{2}x - \frac{1}{3}x = 200$. Solving for x results to 1200. Then 1200 - 150 = 1050. Got the answer but maybe it's just coincidence as I think the 150 should have been part of the equation when solving for x and just subtracting it from the solved value of x looks illogical.

Attempt 3: From the 2nd and 3rd sentence, it states that he spends half of his money, then one-third of what remains for the brownies. It means that if he has 1 dollar, he spends 1/2 of it then 1/3 of it, there will be 1/6 left of his total money. But then the problem continued which states he spends 150 on other pastries. Tried to insert and use $\frac{1}{6}x$ to the equations but no luck.

Any help would be appreciated, thank you. :)

Revel bars $\frac{1}{2}x$, remains $R = \frac{1}{2}x$.
So, triple chocolate is a third of remains. $\frac{1}{3} R = \frac{1}{3} *\frac{1}{2}x=\frac{1}{6}x$
The total sum will be $x$ $$\frac{1}{2}x + \frac{1}{6}x+150+200 = x$$ $$\frac{2}{3}x + 350 = x$$ $$\frac{1}{3}x = 350$$ $$x = 1050$$