Let's break down the problem step-by-step to find the appropriate coefficient for [tex]\( t \)[/tex] in the equation [tex]\( 18 + ? t = 24 \)[/tex]:
1. Understand the Problem:
- We have a cylindrical container with a height of 24 inches.
- The current height of the water in the container is 18 inches.
- Water drips into the container at a rate which increases the water level by 2 inches per hour.
- We need to determine the coefficient of [tex]\( t \)[/tex] in the equation [tex]\( 18 + ? t = 24 \)[/tex], where [tex]\( t \)[/tex] represents the number of hours it takes to fill the container to 24 inches.
2. Set up the Equation:
- Initially, the water level is 18 inches.
- Let [tex]\( t \)[/tex] be the number of hours the faucet drips.
- The water level increases by 2 inches per hour.
- Thus, the increase in water level after [tex]\( t \)[/tex] hours is [tex]\( 2t \)[/tex].
3. Formulate the Equation:
- The total water height after [tex]\( t \)[/tex] hours can be expressed as:
[tex]\[
\text{Initial height} + \text{increase in height} = 18 + 2t
\][/tex]
- We know the target height is 24 inches, so we set up the equation:
[tex]\[
18 + 2t = 24
\][/tex]
4. Identify the Coefficient of [tex]\( t \)[/tex]:
- In the equation [tex]\( 18 + 2t = 24 \)[/tex], the coefficient of [tex]\( t \)[/tex] is the number that multiplies [tex]\( t \)[/tex].
5. Find the Coefficient:
- From the equation [tex]\( 18 + 2t = 24 \)[/tex], it is evident that the coefficient of [tex]\( t \)[/tex] is [tex]\( 2 \)[/tex].
Therefore, the number that should be the coefficient of [tex]\( t \)[/tex] is:
[tex]\[
\boxed{2}
\][/tex]
