The problem presented is about a swimming pool that is being drained at a constant rate of 15 gallons per minute. The pool initially holds 1,200 gallons of water, and the question asks for the equation that represents the amount of water, $g$, left in the pool after $t$ minutes.

Steps to solve:

• The pool starts with 1,200 gallons.
• Every minute, 15 gallons are drained.

So the total water left, $g$, in the pool after $t$ minutes can be expressed as: $g = 1200 - 15t$ Where:

• $1200$ is the initial amount of water,
• $15t$ is the amount of water drained after $t$ minutes (since 15 gallons are drained every minute).

Thus, the equation for the amount of water left is: $g = 1200 - 15t \quad \text{or} \quad g = -15t + 1200$

Answer:

The correct answer is C: $g = -15t + 1,200$.

Let me know if you need further explanation or have any questions!

Here are some additional questions related to this problem:

1. What would the equation be if the draining rate were 10 gallons per minute instead of 15?
2. How much water is left in the pool after 30 minutes of draining?
3. How many minutes will it take to empty the pool completely?
4. How would the equation change if water was being added instead of drained?
5. What is the physical meaning of the slope and intercept in the equation?

Tip:

When interpreting word problems, identify the initial quantity and the rate of change to build your equation.