Question

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.
A. 3d + 2 > 15, where d is the number of days.
B. 3d + 2 < 15, where d is the number of days.
C. 2d + 3 > 15, where d is the number of days.
D. 2d + 3 < 15, where d is the number of days.

Answer 1

To determine how many days it will take for at least 15 people to sign up for the event, we start by recognizing the current number of people signed up and the expected rate of new sign-ups.

Currently, 3 people have signed up, and the library expects an additional 2 people to sign up each day. Let \( d \) represent the number of days after today.

The total number of people signed up after \( d \) days can be expressed as the initial 3 people plus the additional 2 people per day over \( d \) days:
\[ \text{Total number of people} = 3 + 2d \]

To ensure the library can run the event, this number needs to be at least 15:
\[ 3 + 2d \ge 15 \]

Now, let's isolate \( d \) by solving the inequality:
1. Subtract 3 from both sides:
\[ 2d \ge 12 \]
2. Divide by 2:
\[ d \ge 6 \]

Therefore, the library will be sure it can run the event after at least 6 days.

The inequality used to solve this problem is:
\[ 2d + 3 > 15 \]

Thus, the correct answer is:
C. \( 2d + 3 > 15 \)