Jimmy gave his mother $1200 of his salary. He gave $\frac{5}{8}$ of the remainder of his salary to his brother and had $\frac{1}{4}$ of his salary left. What was Jimmy's salary? Answer : $ ___

1. Determine the fraction of the remainder that Jimmy had left

Jimmy gave $\frac{5}{8}$ of the remainder to his brother.
Fraction of remainder left = $1 - \frac{5}{8} = \frac{3}{8}$

2. Relate the fraction of the remainder to the fraction of the total salary

We are given that he had $\frac{1}{4}$ of his total salary left.
So, $\frac{3}{8}$ of the remainder = $\frac{1}{4}$ of the total salary.
Let the remainder be $R$ and total salary be $S$.
$\frac{3}{8} R = \frac{1}{4} S$
$R = \frac{1}{4} \times \frac{8}{3} S = \frac{2}{3} S$

3. Find the fraction of the total salary given to his mother

The amount given to his mother is the difference between the total salary and the remainder.
Fraction given to mother = $1 - \frac{2}{3} = \frac{1}{3}$ of the total salary.

4. Calculate the total salary

$\frac{1}{3}$ of total salary = $\char36{}1200$
Total salary = $\char36{}1200 \times 3 = \char36{}3600$