Final answer:
Hannah needs to sell at least 5 T-shirts and 3 hats to reach her goal of making at least $80 at a craft fair, given the T-shirts are $12 each and hats are $8 each.
Step-by-step explanation:
Hannah is making T-shirts and hats to sell at a craft fair with the goal of making at least $80. Knowing that she will sell each T-shirt for $12 and each hat for $8, and that she is sure to sell at least 5 T-shirts, we can set up an inequality to represent her situation. The inequality will help us figure out how many additional T-shirts and hats Hannah needs to sell in order to reach her target of $80.
Let T represent the total number of T-shirts sold (with T ≥ 5) and H represent the total number of hats sold. The inequality representing Hannah's goal can be written as:
12T + 8H ≥ 80
Since Hannah is sure she will sell at least 5 T-shirts, we substitute 5 for T, yielding:
12(5) + 8H ≥ 80
Hence, her situation is modeled by the inequality:
60 + 8H ≥ 80
We can then solve for H:
8H ≥ 80 - 60
8H ≥ 20
H ≥ 2.5
Since Hannah can't sell half a hat, she'll need to sell at least 3 hats. Therefore, Hannah needs to sell at least 5 T-shirts and 3 hats to make a minimum of $80 at the craft fair.