Let's break down the solution to this problem step-by-step.
1. Understanding the problem:
- The museum charges [tex]\( \$ 25 \)[/tex] per adult and [tex]\( \$ 12 \)[/tex] per child.
- The total revenue for the day is [tex]\( \$ 9,014 \)[/tex].
- The total number of guests is 450.
2. Formulating the equations:
- Let [tex]\( x \)[/tex] be the number of children.
- Let [tex]\( y \)[/tex] be the number of adults.
We have two equations based on the information given:
[tex]\[
12x + 25y = 9014
\][/tex]
[tex]\[
x + y = 450
\][/tex]
3. Solving the system of equations:
First, we'll solve these equations to find [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
The solution to these equations is:
[tex]\[
x = 172 \quad \text{(number of children)}
\][/tex]
[tex]\[
y = 278 \quad \text{(number of adults)}
\][/tex]
4. Graphing the solution:
- Now, we need to place a point on the graph representing the solution to the system of equations.
- On the graph, the x-axis represents the number of children, and the y-axis represents the number of adults.
Solution:
- Point on the graph: [tex]\( (172, 278) \)[/tex]
- Number of children: 172
- Number of adults: 278
So, the approximate number of guests that were children that day is [tex]\( 172 \)[/tex], and the approximate number of guests that were adults is [tex]\( 278 \)[/tex]. This completes our detailed step-by-step solution to the problem.
