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Drag the point and numbers to the correct location on the image. Not all numbers will be used.

A local museum charges [tex]$\$[/tex] 25[tex]$ per adult and $[/tex]\[tex]$ 12$[/tex] per child for admission fees. At the end of the day, the museum made [tex]$\$[/tex] 9,014[tex]$ in total admission revenue, not including sales tax, and had a total of 450 guests.

The system of equations below can be used to model the number of guests that were children, $[/tex]x[tex]$, and the number of guests that were adults, $[/tex]y$.
[tex]\[
\begin{aligned}
12x + 25y & = 9,014 \\
x + y & = 450
\end{aligned}
\][/tex]

1. Place a point on the graph representing the solution to the system of equations. Notice that one of the equations in the system has already been graphed.

2. Determine the approximate number of guests that were children and the approximate number of guests that were adults for that day.



Answer :

GinnyAnswer
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.

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