17. In a college art class, 76 students are painting a mural on one wall of the campus amphitheater. The wall has been divided into 23 sections, and each section will be painted by a group of either 2 or 4 students. How many more sections will be painted by a group of 4 students than by a group of 2 students? A) 6 B) 7 C) 8 D) 9

To solve this, let’s denote the number of sections painted by groups of 2 students as \( x \) and those painted by groups of 4 students as \( y \). We have the equations: 1. \( x + y = 23 \) (total sections) 2. \( 2x + 4y = 76 \) (total students) From the first equation, we can express \( y \) in terms of \( x \): \( y = 23 - x \) Now, substitute this into the second equation: \( 2x + 4(23 - x) = 76 \) Expanding: \( 2x + 92 - 4x = 76 \) Combining like terms gives us: \( -2x + 92 = 76 \) Solving for \( x \): \( -2x = 76 - 92 \) \( -2x = -16 \) \( x = 8 \) Now, substituting \( x \) back to find \( y \): \( y = 23 - 8 = 15 \) So, \( y - x = 15 - 8 = 7 \). The answer is B) 7. Now, let's take a dive into even more interesting aspects around mural painting and group dynamics! The tradition of collaborative mural painting dates back to ancient civilizations, where communities came together to create art that reflected their values and stories. It’s a beautiful way to not only beautify public spaces but also foster teamwork, as artists provide diverse perspectives that come together in a single artwork. Working in groups brings its own challenges! It can be tricky coordinating schedules and agreeing on a unified vision. A tip? Assign roles based on individual strengths—someone could handle logistics while others focus on the artistic design. Regular check-ins help keep everything on track and ensure every voice is heard!