Let's find the coefficient of [tex]\( t \)[/tex] in the equation [tex]\( 18 + ?t = 24 \)[/tex].
Here is how we determine it:
1. Initial Condition: The container is currently filled to a height of 18 inches.
2. Desired Final Condition: The container should be filled to a height of 24 inches.
We start by determining how much more water is needed to reach the desired height.
3. Difference in Water Level:
[tex]\[
24 \text{ inches} - 18 \text{ inches} = 6 \text{ inches}
\][/tex]
Now, we know the water level needs to increase by 6 inches to fill the container.
4. Rate of Increase: The water level increases by 2 inches per hour.
To find the number of hours, [tex]\( t \)[/tex], required to fill the remaining 6 inches, we set up the equation:
[tex]\[
18 + t \times ( \text{rate of increase}) = 24
\][/tex]
Substituting the rate of increase:
[tex]\[
18 + t \times 2 = 24
\][/tex]
So, the coefficient of [tex]\( t \)[/tex] must be what we multiplied [tex]\( t \)[/tex] by in our equation, which is 2.
Answer: The coefficient of [tex]\( t \)[/tex] is 2.
