A swimming pool is being drained at a constant rate of 1515 gallons per minute. The pool initially holds 1,2001,200 gallons of water.

Which equation represents the amount of water, gg, left in the pool after tt minutes?

A.t=−15g+1,200t=−15g+1,200

B.g=15t−1,200g=15t−1,200

C.g=−15t+1,200g=−15t+1,200

D.t=15g+1,200t=15g+1,200


To solve this, let's break it down:

- The pool is being drained at a constant rate of **1515 gallons per minute**.
- The initial amount of water in the pool is **1,200 gallons**.
- We need to find the equation that describes how much water, \( g \), is left in the pool after \( t \) minutes.

### Step 1: Understand the rate of change.
The water is decreasing by **1515 gallons per minute**, which means that the amount of water in the pool decreases linearly with time. So, the rate of change of water is **negative** because the pool is losing water.

### Step 2: The equation form.
Since the pool is initially full with 1,200 gallons, we can write the general equation for this linear relationship as:

\[
g = \text{{initial amount}} - (\text{{rate of change}}) \times t
\]

Substituting the values:

\[
g = 1200 - 1515t
\]

### Step 3: Check the options.
Now, looking at the choices, the correct form should be:

\[
g = -1515t + 1200
\]

This corresponds to **option C**, which is:

\[
\boxed{g = -1515t + 1200}
\]

### Conclusion:
The correct answer is **C**: \( g = -1515t + 1200 \).

Would you like further clarification or more details?

Here are 5 related questions to expand on this topic:
1. How much water will be left after 10 minutes?
2. How long will it take for the pool to be completely drained?
3. What would happen if the draining rate were doubled?
4. How does the slope of the line in the equation relate to the draining process?
5. What if the pool started with 2,000 gallons instead of 1,200 gallons?

**Tip**: Linear equations in the form \( y = mx + b \) describe a relationship where \( m \) is the rate of change and \( b \) is the starting value.

A swimming pool is being drained at a constant rate of 1515 gallons per minute. The pool initially holds 1,200 gallons of water. Which equation represents the amount of water, g, left in the pool after t minutes?

Discover how to model the water drainage of a swimming pool with the linear equation g = -1515t + 1200. This example explains the relationship between time and water volume and is ideal for students in Grades 6-8.

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