https://file.aiquickdraw.com/mathbot/file/1729022069693x727hvlj.jpg

Let's analyze the problem given in the image:

The manager purchased a total of 21 items (coffee mugs and key chains). The costs are:
- Each coffee mug: $8.50
- Each key chain: $2.75

The manager spent a total of $132.50. We need to determine how many coffee mugs were purchased.

Let:
- $ x $ = number of coffee mugs
- $ y $ = number of key chains

We have two equations based on the information:
1. $ x + y = 21 $ (total number of items)
2. $ 8.50x + 2.75y = 132.50 $ (total cost)

Now, let's solve this system of equations.

1. Solve the first equation for $ y $:
   \[
   y = 21 - x
   \]

2. Substitute $ y = 21 - x $ into the second equation:
   \[
   8.50x + 2.75(21 - x) = 132.50
   \]

3. Simplify and solve for $ x $:
   \[
   8.50x + 57.75 - 2.75x = 132.50
   \]
   \[
   5.75x + 57.75 = 132.50
   \]
   \[
   5.75x = 74.75
   \]
   \[
   x = 13
   \]

So, the manager purchased **13 coffee mugs**.

Would you like more details on this solution, or do you have any questions? Here are some related questions you might find useful:

1. How many key chains did the manager purchase?
2. How would the answer change if the total cost was different?
3. What if each coffee mug was priced differently, say $10 each?
4. Can we solve this problem graphically?
5. How does the method change if the problem involves more items?

**Tip:** When solving word problems with systems of equations, always start by identifying what each variable represents and then set up equations based on the problem's conditions.

A manager purchased a total of 21 coffee mugs and key chains. Each coffee mug cost $8.50, and each key chain cost $2.75. If the manager spent a total of $132.50, how many coffee mugs did the manager purchase?

Learn how to solve a system of equations to find out how many coffee mugs were purchased when a manager buys 21 items including coffee mugs and key chains, spending a total of $132.50. Each mug costs $8.50, while each key chain costs $2.75. Suitable for students in Grades 7-10.

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