Question

the library needs at least 15 people to sigh 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

Answer 1

To solve this problem, we can set up an inequality based on the current number of sign-ups and the rate of new sign-ups per day.

Let $d$ represent the number of days until the event. The library currently has 3 sign-ups and expects 2 more people to sign up each day. Therefore, the total number of sign-ups after $d$ days can be represented by the expression:

$$3+2d$$

The library needs at least 15 people to sign up, so we can set up the following inequality:

$$3+2d\ge 15$$

Now, we can solve for $d$:

1. Subtract 3 from both sides: $$2d\ge 12$$

2. Divide both sides by 2: $$d\ge 6$$

So, the library will be sure it can run the event after 6 days.