https://file.aiquickdraw.com/mathbot/file/1726518604158wk1qqpii.jpg

The problem asks to compare the costs of buying baseball caps from two different companies, and we need to determine which inequality represents when **Company X** is cheaper than **Company Y**.

- **Company X** charges a $50 fee plus $7 per cap.
- **Company Y** charges a $30 fee plus $9 per cap.

Let **x** represent the number of caps.

For **Company X**, the cost is:  
\[ C_X = 50 + 7x \]

For **Company Y**, the cost is:  
\[ C_Y = 30 + 9x \]

To find when **Company X** is cheaper than **Company Y**, we need the inequality where **Company X's** cost is **less** than **Company Y's** cost:  
\[ 50 + 7x < 30 + 9x \]

Now, simplifying this inequality:
1. Subtract 7x from both sides:
   \[ 50 < 30 + 2x \]
2. Subtract 30 from both sides:
   \[ 20 < 2x \]
3. Divide both sides by 2:
   \[ 10 < x \]

Thus, **Company X** will be cheaper when the number of caps **x** is greater than 10.

The correct inequality from the options is:  
\[ 50 + 7x < 30 + 9x \]

Let me know if you'd like further details!

Here are 5 related questions for more practice:
1. What is the total cost for Company X when buying 12 caps?
2. How many caps would make the cost of Company X and Company Y equal?
3. If Company X charged $8 per cap instead of $7, how would the inequality change?
4. What happens to the inequality if Company Y's fee increases to $40?
5. How would the solution change if the per cap cost for Company Y was $8 instead of $9?

**Tip**: When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number!

A manager is comparing the cost of buying baseball caps from two different companies. Company X charges a $50 fee plus $7 per cap. Company Y charges a $30 fee plus $9 per cap. Which inequality can be used to determine for what number of caps Company X is cheaper?

Learn how to compare costs between two companies using inequalities. This problem demonstrates how to set up and solve a linear inequality, determining when Company X is cheaper than Company Y. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation