Question

katie wants to collect over 100 seashells. she already has 34 seashells in her collection. each day, she finds 12 more seashells on the beach. katie can use fractions of days to find seashells. write an inequality to determine the number of days, d, it will take katie to collect over 100 seashells. graph the solution set to this inequality. you might need: calculator

Explanation:

Step1: Set up the inequality

Let \(d\) be the number of days. She already has \(34\) seashells and finds \(12\) per day. So the total is \(34 + 12d\). She wants over \(100\), so \(34+12d>100\).

Step2: Solve the inequality

Subtract \(34\) from both sides: \(12d>100 - 34\), so \(12d>66\).
Divide both sides by \(12\): \(d>\frac{66}{12}=\frac{11}{2}=5.5\).

Answer:

The inequality is \(34 + 12d>100\), and the solution is \(d>5.5\). On the number - line, we have an open circle at \(d = 5.5\) (since \(d = 5.5\) is not included in the solution) and an arrow pointing to the right (towards larger values of \(d\)).