1. **State the problem:** We need to find the price of a senior citizen ticket ($y$) and a child ticket ($x$) given two days of ticket sales. 2. **Write the system of equations:** From the problem: - Day 1: $3y + x = 38$ - Day 2: $3y + 2x = 52$ 3. **Solve the system by elimination:** Subtract the first equation from the second: $$3y + 2x - (3y + x) = 52 - 38$$ $$3y + 2x - 3y - x = 14$$ $$x = 14$$ 4. **Substitute $x=14$ into the first equation:** $$3y + 14 = 38$$ $$3y = 38 - 14$$ $$3y = 24$$ 5. **Solve for $y$:** $$y = \frac{24}{3} = 8$$ **Final answer:** - Price of a senior citizen ticket $y = 8$ - Price of a child ticket $x = 14$