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. 0 1 2 3 4 5 6 7 8 9 10 switch direction make circle open

Explanation:

Step1: Define total shells

Total shells = 34 + 12d (34 existing, 12/day)

Step2: Set up inequality

Total > 100 → 34 + 12d > 100

Step3: Solve for d

Subtract 34: 12d > 66 → d > 5.5

Step4: Graph the solution

Open circle at 5.5, shade right.

Answer:

Inequality: $34 + 12d > 100$
Graph: Open circle at 5.5 on number line, blue line extending right from 5.5.