A swimming pool is being drained at a constant rate of 15
 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?
A.t=−15g+1,200

B.g=15t−1,200

C.g=−15t+1,200

D.t=15g+1,200


Let's break this problem down step-by-step. 

We are given:
- **Rate of drainage**: 15 gallons per minute (constant).
- **Initial water**: 1,200 gallons.
- We need to find an equation that expresses the **amount of water \(g\)** left in the pool after \(t\) minutes.

### Step 1: Understanding the relationship
- At **\(t = 0\)**, the pool has 1,200 gallons.
- For every **minute** \(t\), 15 gallons are removed, meaning the amount of water decreases linearly.

The decrease in water can be expressed as:
\[
\text{Water left} = \text{Initial amount} - (\text{Rate} \times \text{Time})
\]
\[
g = 1,200 - 15t
\]

### Step 2: Rewriting the equation  
The correct form matches:
\[
g = -15t + 1,200
\]

This equation tells us that as time \(t\) increases, the amount of water \(g\) decreases by 15 gallons per minute.

### Step 3: Identify the correct option  
The correct option is:

**C. \(g = -15t + 1,200\)**

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Would you like to see more examples of similar problems? 

Here are 5 follow-up questions to practice:  
1. How much water will be left after 30 minutes?  
2. How long will it take to completely drain the pool?  
3. What would the equation be if the pool started with 1,500 gallons instead?  
4. If the rate of drainage was 20 gallons per minute, how would the equation change?  
5. What does the slope of the equation represent in this problem?  

**Tip:** The slope in a linear equation often represents the rate of change—in this case, the gallons lost per minute.

A swimming pool is being drained at a constant rate of 15 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?

This math problem demonstrates how to calculate the amount of water left in a pool after t minutes, given a constant drainage rate of 15 gallons per minute. Learn how to represent the relationship with a linear equation: g = -15t + 1,200. Suitable for Grades 6-8.

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