A business has $25,000 to spend on training sessions for its employees. It wants 45 of its employees to attend. The business wants to send as many employees as it can to a technology training. The technology training costs $1,000 per person. The customer service training costs $500 per person. Create a system of equations that models how many of each type of training the business should purchase. (1 point)

1,000x + 500y = 45
x + y = 25,000

1,000x + 500y = 25,000
x + y = 45

1,000x + y = 45
x + 500y = 25,000

x + 500y = 45
1,000x + y = 25,000


To model how many of each type of training the business should purchase, we need to define variables and set up the equations based on the problem statement.

Let's define:
- $ x $ = number of employees attending the technology training.
- $ y $ = number of employees attending the customer service training.

We have two constraints:

1. **Cost constraint**: The total amount the business can spend on training is $25,000. The technology training costs $1,000 per person, and the customer service training costs $500 per person. This gives us the equation:
   \[
   1000x + 500y = 25000
   \]

2. **Employee constraint**: The business wants 45 employees to attend the training sessions in total. This gives us the equation:
   \[
   x + y = 45
   \]

So, the correct system of equations is:

\[
\begin{cases}
1000x + 500y = 25000 \\
x + y = 45
\end{cases}
\]

Among the provided options, this system corresponds to:

**Option 2:**
\[
1000x + 500y = 25000
\]
\[
x + y = 45
\]

Would you like to see the solution to this system of equations or need further details?

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Here are 5 relative questions:
1. How do you solve this system of equations using substitution?
2. How do you solve this system using the elimination method?
3. What happens if the cost of customer service training changes to $600 per person?
4. How would the system change if the business had a different total budget, like $30,000?
5. How many employees would attend each training if both training sessions had the same cost per person?

**Tip:** When dealing with systems of equations, it's helpful to first express both constraints clearly, like budget and total participants, to set up the equations accurately.

A business has $25,000 to spend on training sessions for its employees. It wants 45 of its employees to attend. The business wants to send as many employees as it can to a technology training. The technology training costs $1,000 per person. The customer service training costs $500 per person. Create a system of equations that models how many of each type of training the business should purchase.

Explore how to model a business scenario using systems of linear equations. Learn to allocate a $25,000 budget for technology and customer service training for 45 employees. This problem involves key algebraic concepts and is suitable for students in Grades 9-10.

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