1. **State the problem:** We need to find the price of a senior citizen ticket ($x$) and a child ticket ($y$) given two days of sales: - Day 1: 1 senior ticket and 6 child tickets sold for a total of 100. - Day 2: 1 senior ticket and 2 child tickets sold for a total of 40. 2. **Write the system of equations:** $$\begin{cases} x + 6y = 100 \\ x + 2y = 40 \end{cases}$$ 3. **Use elimination or substitution to solve:** Subtract the second equation from the first: $$ (x + 6y) - (x + 2y) = 100 - 40 $$ $$ x + 6y - x - 2y = 60 $$ $$ 4y = 60 $$ 4. **Solve for $y$:** $$ y = \frac{60}{4} $$ $$ y = 15 $$ 5. **Substitute $y=15$ into the second equation to find $x$:** $$ x + 2(15) = 40 $$ $$ x + 30 = 40 $$ $$ x = 40 - 30 $$ $$ x = 10 $$ 6. **Check if $x=10$ and $y=15$ are in the possible answers:** - Senior citizen ticket price $x=10$ is in the list. - Child ticket price $y=15$ is in the list. **Final answer:** - Senior citizen ticket price: $10$ - Child ticket price: $15$