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.

Explanation:

Step1: Define total seashells

Total seashells = Initial + Daily * Days. So \( 34 + 12d \).

Step2: Set up inequality

She wants over 100, so \( 34 + 12d > 100 \).

Step3: Solve for \( d \)

Subtract 34: \( 12d > 66 \). Divide by 12: \( d > \frac{66}{12} = 5.5 \).

Step4: Graph the solution

On the number line, open circle at 5.5 (since \( d > 5.5 \)), arrow to the right. The graph should have an open circle between 5 and 6 (or at 5.5) and the line shaded to the right.

Answer:

Inequality: \( 34 + 12d > 100 \)
Graph: Open circle at \( 5.5 \) (or between 5 and 6) on the number line, shaded to the right (towards greater than 5.5).