1. **State the problem:** We have total tickets sold = 100 and total money collected = 590. 2. Let $a$ be the number of adult tickets and $c$ be the number of child tickets. So, we have two equations: $$a + c = 100$$ $$7.5a + 3.5c = 590$$ 3. From the first equation, express $c$ in terms of $a$: $$c = 100 - a$$ 4. Substitute $c$ into the second equation: $$7.5a + 3.5(100 - a) = 590$$ 5. Expand and simplify: $$7.5a + 350 - 3.5a = 590$$ $$4a + 350 = 590$$ 6. Solve for $a$: $$4a = 590 - 350$$ $$4a = 240$$ $$a = \frac{240}{4} = 60$$ 7. Find $c$ using $c = 100 - a$: $$c = 100 - 60 = 40$$ **Final answer:** - Number of adult tickets sold: 60 - Number of child tickets sold: 40