- The table calculations yield \(23 + 61 = 84\), \(61 - 23 = 38\), and the equation \(? - 61 = 23\) results in \(\boxed{84}\).
- For the subway problem, the equations are \(47 + S = 83\) and \(83 - 47 = S\), showing that \(\boxed{36}\) people stand.
- For the bike problem, the relation \(A = 50 - 18\) shows that Anwar rides \(\boxed{32}\) miles.
Explanation
- Problem Analysis
The problem asks for solutions to three arithmetic expressions in a table and two word problems.
- Table Problems:
- Evaluate \(23 + 61\).
- Evaluate \(61 - 23\).
- Solve the equation \(? - 61 = 23\) for the missing value.
- Subway Problem:
- Total passengers = \(83\).
- Seated passengers = \(47\).
- Standing passengers = \(S\).
- We need an addition equation and a subtraction equation to find \(S\).
- Bike Problem:
- Santo's miles = \(50\).
- Anwar's miles = \(A\).
- Relation: Santo rides \(18\) more miles than Anwar, so \(50 = A + 18\). We need to find \(A\).
- Step-by-Step Calculations
- Table Calculations:
- Addition: \(23 + 61 = 84\).
- Subtraction: \(61 - 23 = 38\).
- Equation: \(? - 61 = 23 \implies ? = 23 + 61 = 84\).
- Subway Problem:
- We know that seated plus standing equals total passengers: \(47 + S = 83\).
- We also know that total minus seated equals standing: \(83 - 47 = S\).
- Calculating the number of standing passengers: \(83 - 47 = 36\).
- Bike Problem:
- The relationship is \(S = A + 18\). Given \(S = 50\), we have \(50 = A + 18\).
- Solving for \(A\): \(A = 50 - 18 = 32\). Anwar rode \(32\) miles.
- Conclusion and Final Answers
The results for the requested problems are:
- Table results: \(23 + 61 = 84\), \(61 - 23 = 38\), and the missing value is \(84\).
- Subway problem: Addition equation is \(47 + S = 83\), subtraction equation is \(83 - 47 = S\), and the number of people standing is \(\boxed{36}\).
- Bike problem: Anwar rode \(\boxed{32}\) miles.
Examples
These basic arithmetic operations and algebraic relationships are fundamental in daily life. For instance, knowing how to balance a budget requires addition and subtraction (like the subway and table problems), while comparing distances or quantities is essential for travel planning or resource management (like the bike problem). These skills form the foundation for more complex mathematical modeling used in engineering, economics, and logistics.