Admission to a Museum is \( \$ 30 \) for adults and \( \$ 20 \) for students. The freshman class is attending a field trip with teacher chaperones. Mr. Frees collects \( \$ 5220 \) total from teachers and students, and 256 total people go on the field trip. How many students and teachers attended? Use \( s \) for \# of students and \( a \) for \# of adults A) Write the equation representing the total number of people who went to the Museum B) Write the equation representing the total amount of money collected Now solve your system on your own paper C) Number of students attending: D) Number of adults attending:

Let's denote the number of students as \( s \) and the number of adults as \( a \). A) The total number of people who went to the Museum can be represented by the equation: \[ s + a = 256 \] B) The total amount of money collected can be represented by the equation: \[ 20s + 30a = 5220 \] Now, we have a system of two equations: 1. \( s + a = 256 \) 2. \( 20s + 30a = 5220 \) We can solve this system of equations to find the number of students and adults attending the field trip. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}s+a=256\\20s+30a=5220\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}a=256-s\\20s+30a=5220\end{array}\right.\) - step2: Substitute the value of \(a:\) \(20s+30\left(256-s\right)=5220\) - step3: Simplify: \(-10s+7680=5220\) - step4: Move the constant to the right side: \(-10s=5220-7680\) - step5: Subtract the numbers: \(-10s=-2460\) - step6: Change the signs: \(10s=2460\) - step7: Divide both sides: \(\frac{10s}{10}=\frac{2460}{10}\) - step8: Divide the numbers: \(s=246\) - step9: Substitute the value of \(s:\) \(a=256-246\) - step10: Simplify: \(a=10\) - step11: Calculate: \(\left\{ \begin{array}{l}a=10\\s=246\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}a=10\\s=246\end{array}\right.\) - step13: Rewrite: \(\left(a,s\right) = \left(10,246\right)\) The solution to the system of equations is: - Number of students attending: \( s = 246 \) - Number of adults attending: \( a = 10 \) Therefore, 246 students and 10 adults attended the field trip.