Katie wants to collect over 100 seashells. she already has 34 seashells in her collection. each day, she finds 12 more seashells on beach. katie can use fractions of days to find seashells. write an inequality to determine the number of days, dd, it will take katie to collect over 100 seashells

The inequality that can be used to determine the number of days,d, it will take Katie to collect over 100 seashells is 34 + 12d > 100

Given:

Total number of shells = greater than 100

Shells already collected = 34

Additional shells collected per day = 12

let

d = number of days

The inequality:

Shells already collected + (Additional shells collected per day × number of days) > Total number of shells

34 + (12 × d) > 100

34 + 12d > 100

12d > 100 - 34

12d > 66

d > 66 / 12

d > 5 1/2 days

Therefore, the number of days, d, it will take Katie to collect over 100 seashells is 5 1/2 days

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Step-by-step explanation:

Let d be the number of days.

We have been that each day Katie finds 12 more seashells on beach, so after collecting shells for d days Katie will have 12d shells.  

We are also told that Katie already has 34 seashells in her collection, so total number of shells in Katie collection after d days will be:

As Katie wants to collect over 100 seashells, so the total number of shells collected in d days will be greater than 100. We can represent this information in an inequality as:

Therefore, the inequality can be used to find the number of days, d, it will take Katie to collect over 100 seashells.

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