The admission fee at an amusement park is \( \$ 3.00 \) for children and \( \$ 6.20 \) for adults. On a certain day, 247 people entered the park, and the admission fees collected totaled \( \$ 1173 \). How many children and how many adults were admitted? number of children equals number of adults equals

Let's denote the number of children as \( c \) and the number of adults as \( a \). Given: - Admission fee for children: $3.00 - Admission fee for adults: $6.20 - Total number of people: 247 - Total admission fees collected: $1173 We can set up the following system of equations based on the given information: 1. \( c + a = 247 \) (Total number of people) 2. \( 3c + 6.2a = 1173 \) (Total admission fees collected) Now, we can solve this system of equations to find the number of children and adults admitted. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}c+a=247\\3c+6.2a=1173\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}a=247-c\\3c+6.2a=1173\end{array}\right.\) - step2: Substitute the value of \(a:\) \(3c+6.2\left(247-c\right)=1173\) - step3: Simplify: \(-3.2c+1531.4=1173\) - step4: Move the constant to the right side: \(-3.2c=1173-1531.4\) - step5: Subtract the numbers: \(-3.2c=-358.4\) - step6: Change the signs: \(3.2c=358.4\) - step7: Divide both sides: \(\frac{3.2c}{3.2}=\frac{358.4}{3.2}\) - step8: Divide the numbers: \(c=112\) - step9: Substitute the value of \(c:\) \(a=247-112\) - step10: Calculate: \(a=135\) - step11: Calculate: \(\left\{ \begin{array}{l}a=135\\c=112\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}a=135\\c=112\end{array}\right.\) - step13: Rewrite: \(\left(a,c\right) = \left(135,112\right)\) The solution to the system of equations is \( a = 135 \) and \( c = 112 \). Therefore, on that day, 112 children and 135 adults were admitted to the amusement park.