Alright, let's go through the problem step by step to identify the coefficient of [tex]\( t \)[/tex] in the equation [tex]\( 18 + ?t = 24 \)[/tex].
1. Understand the current situation:
- The container is currently filled with water to a height of 18 inches.
- The total height of the container is 24 inches.
2. Determine the difference in height:
- To find out how many more inches of water are needed to fill the container, we subtract the current water height from the total height of the container:
[tex]\[
24 \text{ inches} - 18 \text{ inches} = 6 \text{ inches}
\][/tex]
3. Rate of increase:
- The rate at which the water height increases due to the leaky faucet is 2 inches per hour.
4. Set up the equation:
- We need to write an equation that represents the situation. Specifically, we need to find [tex]\( t \)[/tex], the number of hours it will take for the water to fill the container to its full height. The given scenario can be represented as:
[tex]\[
18 + 2t = 24
\][/tex]
5. 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 is multiplied by [tex]\( t \)[/tex]. In this case, the coefficient is 2.
Thus, the number that should be the coefficient of [tex]\( t \)[/tex] is:
[tex]\[
\boxed{2}
\][/tex]
