Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 28 liters per minute. There are 500 liters in the pond to start. Let \( W \) represent the total amount of water in the pond (in liters), and let \( T \) represent the total number of minutes that water has been added. Write an equation relating \( W \) to \( T \). Then use this equation to find the total amount of water after 16 minutes. Equation: Total amount of water after 16 minutes:

To solve the problem, we need to establish the relationship between the total amount of water in the pond \( W \) and the time \( T \) in minutes. 1. **Identify the known conditions:** - Initial amount of water in the pond: 500 liters - Rate of water being added: 28 liters per minute 2. **Write the equation:** The total amount of water \( W \) in the pond after \( T \) minutes can be expressed as: \[ W = 500 + 28T \] This equation states that the total water \( W \) is equal to the initial water (500 liters) plus the amount of water added over \( T \) minutes (which is \( 28T \) liters). 3. **Calculate the total amount of water after 16 minutes:** We will substitute \( T = 16 \) into the equation: \[ W = 500 + 28 \times 16 \] Now, let's perform the calculation for \( 28 \times 16 \): \[ 28 \times 16 = 448 \] Now, substitute this back into the equation for \( W \): \[ W = 500 + 448 = 948 \] Thus, the total amount of water in the pond after 16 minutes is: \[ \text{Total amount of water after 16 minutes: } 948 \text{ liters} \] ### Summary: - **Equation:** \( W = 500 + 28T \) - **Total amount of water after 16 minutes:** 948 liters