https://file.aiquickdraw.com/mathbot/file/1729007725926bvixqsz2.jpg

The problem states:

- The manager bought a total of **21 items** (coffee mugs and key chains).
- The cost of each coffee mug is **$8.50**.
- The cost of each key chain is **$2.75**.
- The total amount spent is **$132.50**.

Let:
- $ x $ = the number of coffee mugs.
- $ 21 - x $ = the number of key chains (since the total number of items is 21).

The total cost equation is:

\[
8.50x + 2.75(21 - x) = 132.50
\]

Now, let's solve this step by step:

1. Expand the equation:

\[
8.50x + 2.75(21 - x) = 132.50
\]

\[
8.50x + 57.75 - 2.75x = 132.50
\]

2. Combine like terms:

\[
(8.50x - 2.75x) + 57.75 = 132.50
\]

\[
5.75x + 57.75 = 132.50
\]

3. Subtract 57.75 from both sides:

\[
5.75x = 132.50 - 57.75
\]

\[
5.75x = 74.75
\]

4. Divide both sides by 5.75:

\[
x = \frac{74.75}{5.75}
\]

\[
x = 13
\]

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

Do you want further details or have any questions?

Here are some related questions to further practice:
1. How many key chains did the manager purchase?
2. What would the total cost be if the manager bought 10 coffee mugs instead?
3. If the price of the key chains increases to $3.00, how does that affect the total cost?
4. What if the manager bought 25 items in total, keeping the same prices—how many mugs would be bought if the total spent is $160?
5. How would the equation change if the price of mugs dropped to $7.00?

**Tip:** When dealing with word problems, always assign variables for unknown quantities and translate the problem step by step into an equation.

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 linear equation involving the purchase of 21 coffee mugs and key chains with a total cost of $132.50. This problem focuses on algebraic concepts suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation