1. **State the problem:** Michael needs to buy 100 kg of chocolate in total, using dark chocolate and milk chocolate. Dark chocolate costs 12 per kg, milk chocolate costs 10 per kg, and he wants to spend 1120 total. 2. **Define variables:** Let $d$ = kilograms of dark chocolate Let $m$ = kilograms of milk chocolate 3. **Write equations based on the problem:** - Total weight equation: $d + m = 100$ - Total cost equation: $12d + 10m = 1120$ 4. **Explain the system:** The first equation ensures the total kilograms of chocolate is 100. The second equation ensures the total cost is 1120. 5. **Final system of equations:** $$\begin{cases} d + m = 100 \\ 12d + 10m = 1120 \end{cases}$$ This system represents the situation described.