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, dd, it will take Katie to collect over 100 seashells.

Answer 1

Answer: The answer is
`34+12d>100.`

Step-by-step explanation: Given that Katie wants to collect more than 100 seashells. She already has 34 seashells in her collection and she finds 12 more seashells on the beach every day. Katie can use fractions of days to find seashells.

The number of days is represented by 'd', which Katie will take to collect over 100 seashells.

The number of seashells Katie will collect in 'd' days will be given by

`34+12* d.`

Since she needs to collect more than 100 seashells, so we have

`34+12* d> 100.`

After solving,

`34+12d> 100\\\\\Rightarrow 12d> 100-34\\\\\Rightarrow 12d> 66\\\\\\\Rightarrow d>5(1)/(2).`

Thus, Katie will need to collect seashells for more than 5.5 days. and the required inequality is

`34+12d> 100.`

Answer 2

Katie won't have more than 100 seashells until the 6th day.

Explanation:

No. of seashells to be collected = 100

Initial number of seashells in the collection = 34

No, of seashells found each day = 12

So, number of seashells collected in d days = 12·d

Total number of seashells collected after d days = 34 + 12·d

Number of days needed by Katie to save more than 100 seashells :

34 + 12·d > 100

Subtracting 34 from both the sides

⇒ 12·d > 66

⇒ d > 5.5

Hence, Katie won't have more than 100 seashells until the 6th day.