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A cylindrical container has a height of 24 inches. Currently, the container is filled with water to a height of 18 inches. A leaky faucet drips into the container, causing the height of the water to increase by 2 inches per hour. The equation below can be used to find [tex]\( t \)[/tex], the number of hours it would take to fill the container.

[tex]\[ 18 + 2t = 24 \][/tex]

What number should be the coefficient of [tex]\( t \)[/tex]?

A. 2
B. 3
C. 18
D. 24

Sagot :

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]
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