1. **State the problem:** Find the price of a senior citizen ticket and the price of a child ticket given the system: $$3y + t = 36$$ $$3y + 2t = 52$$ where $y$ is the price of a senior citizen ticket and $t$ is the price of a child ticket. 2. **Write down the system of equations:** \begin{align*} 3y + t &= 36 \\ 3y + 2t &= 52 \end{align*} 3. **Subtract the first equation from the second to eliminate $3y$:** $$ (3y + 2t) - (3y + t) = 52 - 36 $$ $$ \cancel{3y} + 2t - \cancel{3y} - t = 16 $$ $$ t = 16 $$ 4. **Substitute $t = 16$ back into the first equation:** $$ 3y + 16 = 36 $$ 5. **Solve for $y$:** $$ 3y = 36 - 16 $$ $$ 3y = 20 $$ $$ y = \frac{20}{3} $$ 6. **Interpret the solution:** The price of a senior citizen ticket is $\frac{20}{3} \approx 6.67$ and the price of a child ticket is $16$. **Final answer:** $$ y = \frac{20}{3}, \quad t = 16 $$