Write an inequality that represents all possible combinations of hats, x, and T-shirts, y, in an order that qualifies for free shipping.
Understand the Problem
The question is asking us to formulate an inequality that describes the conditions under which a customer's order qualifies for free shipping based on the cost of hats and T-shirts. We need to consider the cost of hats, T-shirts, and the threshold for free shipping.
Answer
The inequality for free shipping is $x \cdot h + y \cdot t \geq S$.
Answer for screen readers
The inequality that describes the conditions for free shipping is:
$$ x \cdot h + y \cdot t \geq S $$
Steps to Solve
- Identifying Variables
Let's denote the cost of one hat as $h$ and the cost of one T-shirt as $t$.
- Defining the Variables for Quantity
Suppose the customer orders $x$ hats and $y$ T-shirts. The total cost of the order can be expressed as:
$$ \text{Total Cost} = x \cdot h + y \cdot t $$
- Setting the Free Shipping Threshold
Assume there is a threshold amount for free shipping, let's call this threshold $S$. To qualify for free shipping, the total cost must meet or exceed this amount.
- Formulating the Inequality
To express the condition for free shipping, we set up the inequality:
$$ x \cdot h + y \cdot t \geq S $$
This inequality shows that the total cost must be greater than or equal to the free shipping threshold.
The inequality that describes the conditions for free shipping is:
$$ x \cdot h + y \cdot t \geq S $$
More Information
This inequality helps determine if a customer's order qualifies for free shipping based on the costs of hats and T-shirts, ensuring they know how much they need to spend to benefit from this offer.
Tips
- Confusing the total amount with just the cost of either hats or T-shirts alone. Always remember to consider both types of items in the total cost calculation.
