Question 702460
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.