Val's whole-house central air conditioner uses 4,000 watts when running. Val runs the AC 6 hours per summer day. Electricity costs 12 cents per 1 kilowatt-hour. How much does Val's AC cost to run for a summer month of 30 days?
The power consumption of the air conditioner is given as \(4,000\) watts. To calculate energy consumption in kilowatt-hours (kWh), we first convert the power from watts to kilowatts. Since \(1 \text{ kilowatt (kW)} = 1,000 \text{ watts (W)}\), we have:
\[4,000 \text{ W} = \frac{4,000}{1,000} \text{ kW} = 4 \text{ kW}.\]
The air conditioner runs for \(6\) hours each day. The daily energy consumption is the product of the power and the daily running time:
\[4 \text{ kW} \times 6 \text{ hours/day} = 24 \text{ kWh/day}.\]
To find the total energy consumption for a summer month of \(30\) days, we multiply the daily energy consumption by the number of days:
\[24 \text{ kWh/day} \times 30 \text{ days} = 720 \text{ kWh}.\]
Electricity costs \(12\) cents per kilowatt-hour. We multiply the total monthly energy consumption by this rate to find the total cost in cents:
\[720 \text{ kWh} \times 12 \text{ cents/kWh} = 8,640 \text{ cents}.\]
Thus, the total cost for Val to run the air conditioner for the month is \(\boxed{8640}\) cents.
Understanding energy consumption and calculating its costs is a fundamental skill for household budgeting. For example, if you know the wattage of your appliances and the rate your electricity provider charges per kilowatt-hour, you can estimate your monthly utility bills. This helps in identifying high-energy-consuming devices and managing overall energy usage effectively to save on costs, demonstrating the practical application of basic arithmetic and unit conversion in everyday life.