https://file.aiquickdraw.com/mathbot/file/1730142624139mk1lzz3p.jpg

To write an inequality representing all possible combinations of hats ($ x $) and T-shirts ($ y $) that qualify for free shipping, let’s analyze the problem step-by-step.

### Given Information
- Each hat costs $7.
- Each T-shirt costs $10.
- Free shipping is provided if the total order is **over** $100.

### Set Up the Inequality
Let:
- $ x $ = number of hats
- $ y $ = number of T-shirts

The total cost of $ x $ hats and $ y $ T-shirts can be expressed as:
\[
7x + 10y
\]

For free shipping, this total cost must be more than $100. Therefore, we write the inequality as:
\[
7x + 10y > 100
\]

### Answer
Based on the answer options provided in the image, the correct inequality is:

\[
7x + 10y > 100
\]

Would you like further clarification or have any additional questions?

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Here are 5 related questions for further exploration:
1. How would the inequality change if free shipping was given for orders **equal to or over** $100?
2. What would the inequality look like if hats were $5 instead of $7?
3. How could you graph this inequality on a coordinate plane?
4. How many hats and T-shirts could the customer buy if they only have a $100 budget?
5. How does changing the cost of the hats or T-shirts affect the inequality?

**Tip**: When setting up inequalities involving money, make sure to correctly interpret "more than," "less than," or "at least" to avoid mistakes.

A customer is ordering hats and T-shirts from an online store. Each hat costs $7, and each T-shirt costs $10. The customer receives free shipping if the amount of the order is over $100. Write an inequality that represents all possible combinations of hats, x, and T-shirts, y, in an order that qualifies for free shipping.

Learn how to set up an inequality to determine the number of hats and T-shirts a customer can order to qualify for free shipping when hats cost $7 and T-shirts cost $10, and the total order needs to exceed $100. Suitable for Grades 7-9.

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