Answer :
To solve this problem, we need to set up a system of equations based on the information given:
1. Identify the Variables:
- Let [tex]\( a \)[/tex] represent the number of adults.
- Let [tex]\( c \)[/tex] represent the number of children.
2. Create the Equations:
- We know that the total number of people (adults and children) who visited the park is 3806. This gives us the first equation:
[tex]\[
a + c = 3806
\][/tex]
- We also know that the total revenue from admissions was [tex]$55,157. Since adults pay $[/tex]19 each and children pay $9.50 each, our second equation is:
[tex]\[
19a + 9.5c = 55,157
\][/tex]
3. Select the System of Equations:
- Combine the two equations we formed:
[tex]\[
\begin{cases}
a + c = 3806 \\
19a + 9.5c = 55,157
\end{cases}
\][/tex]
This matches Option D from the choices provided.
By solving these two equations, you can find the values of [tex]\( a \)[/tex] and [tex]\( c \)[/tex], which are the numbers of adults and children, respectively, who visited the amusement park that weekend.
1. Identify the Variables:
- Let [tex]\( a \)[/tex] represent the number of adults.
- Let [tex]\( c \)[/tex] represent the number of children.
2. Create the Equations:
- We know that the total number of people (adults and children) who visited the park is 3806. This gives us the first equation:
[tex]\[
a + c = 3806
\][/tex]
- We also know that the total revenue from admissions was [tex]$55,157. Since adults pay $[/tex]19 each and children pay $9.50 each, our second equation is:
[tex]\[
19a + 9.5c = 55,157
\][/tex]
3. Select the System of Equations:
- Combine the two equations we formed:
[tex]\[
\begin{cases}
a + c = 3806 \\
19a + 9.5c = 55,157
\end{cases}
\][/tex]
This matches Option D from the choices provided.
By solving these two equations, you can find the values of [tex]\( a \)[/tex] and [tex]\( c \)[/tex], which are the numbers of adults and children, respectively, who visited the amusement park that weekend.
