Ratio problem to find the woman weekly salary

Question

A woman spend $5/8$ of her weekly salary on rent, and $1/3$ of the remainder on food, leaving $40 available for other expenses. What is the woman's weekly salary ?

I have tried , i am really confused with finding remainder.

Answer 1

Let $x$ be her weekly salary. She spends $\frac58x$ on rent; the remainder is what’s left, so the remainder is $x-\frac58x=\frac38x$. She spends $\frac13$ of that, or $\frac13\cdot\frac38x=\frac18x$, on food; that leaves $\frac38x-\frac18x=\frac14x$ for other expenses. Can you finish it now?

Answer 2

Hints:

$$x-\frac58x-\frac13\left(x-\frac58x\right)=40\iff\left(x-\frac58x\right)\left(1-\frac13\right)=40\iff\frac23\frac38x=40$$

Answer 3

We work backwards.

She spent one-third of the "remainder" (after rent) on food. This means that the $40$ dollars she had left were two-thirds of that remainder. So the remainder was $60$.

This $60$ dollars was the $\frac{3}{8}$ of salary left after paying the rent. So one-eighth of her salary is $20$ dollars, and therefore her salary is $160$.

Remark: The above solution is provided to show that the answer can be found without using "algebra." However, you should use algebra, it is a powerful tool that needs to be mastered.