1. **State the problem:** Rosa wants to exercise a total of 175 minutes. She has already walked 110 minutes. She can do jumping jacks for 1 minute at a time and jog for 10 minutes at a time. We need to find how she can combine jumping jacks and jogging to reach her goal. 2. **Define variables:** Let $x$ be the number of jumping jack sessions (each 1 minute), and $y$ be the number of jogging sessions (each 10 minutes). 3. **Write the equation:** The total exercise time must be 175 minutes: $$110 + 1 \cdot x + 10 \cdot y = 175$$ 4. **Simplify the equation:** $$x + 10y = 175 - 110$$ $$x + 10y = 65$$ 5. **Interpret the equation:** Rosa needs to do a combination of jumping jacks and jogging so that the total minutes from these activities add up to 65. 6. **Find possible solutions:** Since $x$ and $y$ represent counts of sessions, they must be non-negative integers. - For $y=0$, $x=65$ jumping jack sessions. - For $y=1$, $x=65 - 10 = 55$ jumping jack sessions. - For $y=2$, $x=65 - 20 = 45$ jumping jack sessions. ... and so on until $y=6$, $x=65 - 60 = 5$ jumping jack sessions. 7. **Conclusion:** Rosa can reach her goal by doing any combination of jumping jacks and jogging sessions that satisfy $x + 10y = 65$ with $x,y \geq 0$ integers. For example, 5 jumping jack sessions and 6 jogging sessions. **Final answer:** Rosa can do $x$ jumping jack sessions and $y$ jogging sessions such that $$x + 10y = 65$$ where $x,y$ are non-negative integers.