MEGA Elementary Education Multi-Content Practice Test

How can the relationship between Regina's and Sam's weekly running distances be modeled in an equation?

1. r = 3s + 8 - 6

2. s = 2r + 8 + 6

3. 3r + 8 = 2s + 6

4. 2r + 8 = 3s + 6

The correct answer is: 3r + 8 = 2s + 6

To determine how the relationship between Regina's and Sam's weekly running distances can be modeled mathematically, we look for an equation that represents a functional relationship based on their distances. Choosing the correct option involves recognizing the coefficients and constants that represent their distances properly. The correct equation, 3r + 8 = 2s + 6, suggests a particular relationship between the two individuals’ weekly running distances. In this context, 'r' can represent Regina’s distance, and 's' can represent Sam’s distance. In this equation, the left-hand side (3r + 8) indicates that Regina runs a distance that is influenced not only by her own running distance (multiplied by 3, possibly suggesting she runs more than Sam) but also includes an additional constant (8). Similarly, the right-hand side (2s + 6) indicates that Sam's distance also has an associated relationship, where his distance is scaled by a factor of 2 and increased by a constant (6). This format highlights a comparative relationship where both individuals' running distances sync up with their respective coefficients and constants, capturing how Regina's and Sam's distances are correlated through two different ratios expressed in the equation. The other options do not