1. **State the problem:** Kwame spends fractions of his monthly salary on food, rent, and sweets, and after these expenses, he has 90 left. We need to find his total salary, and how much he spent on food and rent. 2. **Define variables:** Let Kwame's monthly salary be $S$. 3. **Calculate amount spent on food:** He spends $\frac{1}{5}$ of $S$ on food, so food expense is $\frac{1}{5}S$. 4. **Calculate remaining after food:** Remaining salary after food is $S - \frac{1}{5}S = \frac{4}{5}S$. 5. **Calculate amount spent on rent:** He spends $\frac{1}{2}$ of the remaining on rent, so rent expense is $\frac{1}{2} \times \frac{4}{5}S = \frac{2}{5}S$. 6. **Calculate remaining after rent:** Remaining after rent is $\frac{4}{5}S - \frac{2}{5}S = \frac{2}{5}S$. 7. **Calculate amount spent on sweets:** He spends $\frac{1}{4}$ of the remaining on sweets, so sweets expense is $\frac{1}{4} \times \frac{2}{5}S = \frac{1}{10}S$. 8. **Calculate remaining after sweets:** Remaining after sweets is $\frac{2}{5}S - \frac{1}{10}S = \frac{4}{10}S - \frac{1}{10}S = \frac{3}{10}S$. 9. **Set remaining equal to 90:** $\frac{3}{10}S = 90$. 10. **Solve for $S$:** Multiply both sides by $\frac{10}{3}$: $$ S = 90 \times \frac{10}{3} = 90 \times \frac{10}{3} = 300 $$ 11. **Calculate amount spent on food:** $\frac{1}{5} \times 300 = 60$. 12. **Calculate amount spent on rent:** $\frac{2}{5} \times 300 = 120$. **Final answers:** - Monthly salary $S = 300$. - Amount spent on food = 60. - Amount spent on rent = 120.