SOLUTION: I have the answer but just cant figure out how to sent up the equations. The answer is 30..... After a girl spends 1/3 of her money and loses 1/2 of the remainder, she then has $

Question 702460: I have the answer but just cant figure out how to sent up the equations.
The answer is 30.....
After a girl spends 1/3 of her money and loses 1/2 of the remainder, she then has $10 left. How much did she start with?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
She starts with x dollars

She spends 1/3 of it, so she has 2/3 of it left. So she now has 2x/3 dollars

She spends half of that, so she spends half of 2x/3 and spends x/3 dollars.

So she has 2x/3 - x/3 = x/3 dollars left.

We're told she has $10 left, so x/3 = 10, which means x = 3*10 = 30

So x = 30, which means she started with $30.

Check:

Start with $30

Spend 1/3 (ie spend $10) to be left with $20

Lose half of $20 to be left with $10

So the answer checks out.
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