The library needs at least 15 people to sign up for an event in order to run it. Currently, 3 people have signed up, and the library expects 2 more people to sign up each day. After how many days will the library be sure it can run the event? Write an inequality that could be used to solve this problem.(1 point) Responses 3d+2≤15 , where d is the number of days. 3 d plus 2 less than or equal to 15 , where d is the number of days. 3d+2≥15 , where d is the number of days. 3 d plus 2 greater than or equal to 15 , where d is the number of days. 2d+3≤15 , where d is the number of days. 2 d plus 3 less than or equal to 15 , where d is the number of days. 2d+3≥15 , where d is the number of days.

Question

GPT-4o mini · Answer

To determine after how many days the library will have at least 15 people signed up for the event, we start with the current number of sign-ups and the expected increase:

Currently, 3 people have signed up.
The library expects 2 more people to sign up each day.

If \(d\) represents the number of days after which we are evaluating the total sign-ups, the total number of sign-ups after \(d\) days can be expressed as:

\[ 3 + 2d \]

We want to find when this total will be at least 15. Therefore, we set up the inequality:

\[ 3 + 2d \geq 15 \]

This is the inequality that can be used to determine how many days it will take for the library to be sure it can run the event.

Therefore, the correct response is:

2d + 3 ≥ 15, where d is the number of days.