Question

Sheila went shopping and spent $120 on a coat. She then used 2/3 of the
remaining money to buy a dress. She was left with 1/5 of her original amount
of money. How much did Sheila have at first?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{original}\mathrm{amount}\mathrm{be}\&\mathrm{x} \\ \mathrm{Spent}\mathrm{on}\mathrm{coat}=\&120 \\ \mathrm{Remaining}\mathrm{money}=\mathrm{x}-120 \\ \mathrm{Also}\mathrm{money}\mathrm{spent}\mathrm{on}\mathrm{dress}=\&\frac{2}{3}\times \left(\mathrm{x}-120\right) \\ \mathrm{Money}\mathrm{left}\mathrm{with}\mathrm{her}=\frac{1}{5}\mathrm{x} \\ \mathrm{Money}\mathrm{she}\mathrm{have}\mathrm{at}\mathrm{first},\mathrm{x}=120+\frac{2}{3}\times \left(\mathrm{x}-120\right)+\frac{1}{5}\mathrm{x} \\ \Rightarrow \mathrm{x}=120+\frac{2}{3}\mathrm{x}-80+\frac{1}{5}\mathrm{x} \\ \Rightarrow \mathrm{x}-\frac{2}{3}\mathrm{x}-\frac{1}{5}\mathrm{x}=40 \\ \Rightarrow \frac{2}{15}\mathrm{x}=40 \\ \Rightarrow \mathrm{x}=\&300 \end{gathered}$$
Regards