https://file.aiquickdraw.com/mathbot/file/1729871885536k6wdbplv.jpg

The problem describes the cost of hats and T-shirts, and asks for an inequality that represents combinations of hats $ x $ and T-shirts $ y $ that qualify for free shipping. Let's break it down:

1. **Hat cost**: Each hat costs $7, so the total cost of hats is $ 7x $.
2. **T-shirt cost**: Each T-shirt costs $10, so the total cost of T-shirts is $ 10y $.
3. **Condition for free shipping**: The total order must be **over** $100 to qualify for free shipping.

Thus, the inequality that represents the condition for free shipping is:

\[
7x + 10y > 100
\]

Based on the image provided, you need to drag the correct values into the boxes. The inequality should be structured as follows:

\[
7x + 10y > 100
\]

Would you like further clarification on any part of the solution, or would you like help with another problem?

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Here are 5 questions to expand your understanding:
1. How would the inequality change if the customer received free shipping on orders **equal to or greater than** $100?
2. If a customer buys 8 hats, how many T-shirts are needed to qualify for free shipping?
3. What would the inequality look like if the hat price increased to $8?
4. How would you graph this inequality in the coordinate plane?
5. Can you represent the same situation using a system of inequalities for different shipping tiers (e.g., free shipping for orders over $100, but a discount for orders between $75-$100)?

**Tip**: When working with inequalities, remember that the direction of the inequality changes if you multiply or divide by a negative number!

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 write an inequality representing combinations of hats and T-shirts that qualify for free shipping on orders over $100. This problem uses linear inequalities and applies algebraic principles, suitable for Grades 6-8.

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