1. **State the problem:** Maria is monitoring two substances with temperatures changing over time. Substance A starts at 97.7 degrees and increases by 1.1 degrees per minute. Substance B starts at 116.9 degrees and decreases by 1.30 degrees per minute. We want to find after how many minutes $m$ the temperatures will be equal. 2. **Write the equation:** Let $T_A$ be the temperature of Substance A and $T_B$ be the temperature of Substance B after $m$ minutes. $$T_A = 97.7 + 1.1m$$ $$T_B = 116.9 - 1.30m$$ We want to find $m$ such that $T_A = T_B$: $$97.7 + 1.1m = 116.9 - 1.30m$$ 3. **Solve the equation:** Combine like terms by adding $1.30m$ to both sides: $$97.7 + 1.1m + 1.30m = 116.9$$ $$97.7 + 2.4m = 116.9$$ Subtract 97.7 from both sides: $$2.4m = 116.9 - 97.7$$ $$2.4m = 19.2$$ Divide both sides by 2.4: $$m = \frac{19.2}{2.4}$$ Calculate the division: $$m = 8$$ 4. **Interpretation:** After 8 minutes, the temperatures of Substance A and Substance B will be the same.