1. **State the problem:** We are given two equations based on the cost of purses and watches: - 1 purse + 1 watch = 27 - 2 purses + 1 watch = 41 We need to find the cost of 1 purse and 1 watch. 2. **Define variables:** Let $p$ be the cost of 1 purse. Let $w$ be the cost of 1 watch. 3. **Write the system of equations:** $$\begin{cases} p + w = 27 \\ 2p + w = 41 \end{cases}$$ 4. **Subtract the first equation from the second:** $$ (2p + w) - (p + w) = 41 - 27 $$ $$ 2p + w - p - w = 14 $$ $$ p = 14 $$ 5. **Substitute $p=14$ into the first equation:** $$ 14 + w = 27 $$ $$ w = 27 - 14 $$ $$ w = 13 $$ 6. **Final answer:** - The cost of 1 purse is $14$. - The cost of 1 watch is $13$.