You are looking at two different computers for your dorm the higher end system uses 1600 watts of power for 8 hours of use and the smaller system 1275 watts for the same amount of time. If your energy costs  a kilowatt-hour, what is the difference in cost over the 8 hours?
The difference in cost is

To find the difference in cost of running the two systems for 8 hours, we will calculate the energy consumed by each system and then determine the cost based on the energy rate.

### Step 1: Convert power from watts to kilowatts
Since energy is usually measured in kilowatt-hours (kWh), we first convert the power used by each system from watts to kilowatts:

- Higher-end system: $ 1600 \, \text{watts} = 1.6 \, \text{kW} $
- Smaller system: $ 1275 \, \text{watts} = 1.275 \, \text{kW} $

### Step 2: Calculate the energy consumption over 8 hours
Now we multiply the power by the number of hours of use (8 hours) to find the total energy consumed by each system:

- Higher-end system: $ 1.6 \, \text{kW} \times 8 \, \text{hours} = 12.8 \, \text{kWh} $
- Smaller system: $ 1.275 \, \text{kW} \times 8 \, \text{hours} = 10.2 \, \text{kWh} $

### Step 3: Calculate the cost for each system
Assuming the cost of electricity is 1 unit per kilowatt-hour (1 kWh = $1):

- Higher-end system: $ 12.8 \, \text{kWh} \times 1 \, \text{dollar/kWh} = 12.8 \, \text{dollars} $
- Smaller system: $ 10.2 \, \text{kWh} \times 1 \, \text{dollar/kWh} = 10.2 \, \text{dollars} $

### Step 4: Find the difference in cost
The difference in cost between the two systems is:

\[
12.8 \, \text{dollars} - 10.2 \, \text{dollars} = 2.6 \, \text{dollars}
\]

### Final Answer:
The difference in cost over 8 hours is **$2.60**.

Would you like more details or have any questions?

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Here are some related questions:
1. What would the difference in cost be over 24 hours?
2. How much energy would each system consume in a week (assuming 8 hours of daily use)?
3. What would the total cost for running each system over a month (30 days) be?
4. How does reducing the usage time by 2 hours impact the cost difference?
5. If energy prices increase by 20%, what would the new cost difference be?

**Tip**: To reduce energy costs, consider using power-saving modes when the computer is idle.

You are looking at two different computers for your dorm. The higher-end system uses 1600 watts of power for 8 hours of use and the smaller system 1275 watts for the same amount of time. If your energy costs 1 dollar per kilowatt-hour, what is the difference in cost over the 8 hours?

Learn how to calculate the difference in cost between two computers based on their energy consumption over 8 hours. This detailed solution covers energy usage, unit conversion, and cost calculation. Perfect for students in Grades 6-8.

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