Hugh works two part-time jobs to save for his college expenses. He earns 10 dollars per hour at a grocery store and 13 dollars per hour babysitting. He wants to earn at least 260 dollars per week. If $x$ represents the number of hours he works at the grocery store and $y$ represents the number of hours he spends babysitting, which inequality correctly models Hugh's goal?

Hugh works at a grocery store earning ${}10$ dollars per hour and babysits for ${}13$ dollars per hour. He uses the inequality ${}10x + 13y \geq 260$ to model his goal of earning at least ${}260$ a week. Match each component of this mathematical model to the real-world value it represents.

Hugh models his goal of earning at least ${}260$ a week from two jobs using the inequality ${}10x + 13y \geq 260$. True or False: In the graph of this inequality, the solid boundary line indicates that combinations of hours earning exactly ${}260$ dollars are included in the solution set.

Hugh is working two jobs—one at a grocery store earning 10 dollars per hour and one babysitting for 13 dollars per hour—to earn at least 260 dollars a week. To find the combinations of hours he can work, he models and graphs the situation using a linear inequality. Arrange the following steps in the correct order to represent this modeling process.

Hugh, an adult learner balancing his studies, earns ${}10$ an hour at a grocery store ($x$) and ${}13$ an hour doing freelance administrative work ($y$). To earn at least ${}260$ a week to cover his expenses, he uses the linear inequality ${}10x + 13y \geq 260$. When graphing this inequality to visualize his work options, any ordered pair (x, y) representing a valid combination of hours will fall either on the solid boundary line or within the ____ region.

Interpreting the Solution Region

Real-World Interpretation of Boundary Lines and Solution Regions