Let x be the initial amount of money. Miss Jones gave 1/4 of her money to charity, which means that the remainder is
[tex]x-\dfrac{1}{4}x=\dfrac{3}{4}x[/tex]
Half of this remainder is given to her mother, so the new remainder is half of the previous one:
[tex]\dfrac{3}{4}x\cdot\dfrac{1}{2}=\dfrac{3}{8}x[/tex]
So, the remaining 240 are 3/8 of what she had at the beginning. This means that she had
[tex]\dfrac{3}{8}x=240 \iff x = \dfrac{240 \cdot 8}{3}=640[/tex]
at the beginning.
