- Determine the monthly cost for each type of bulb: incandescent is \(0.05 \times 150 = \$7.50\), and fluorescent is \(0.02 \times 150 = \$3.00\).
- Find the monthly savings per bulb: \(7.50 - 3.00 = \$4.50\).
- Calculate the total annual savings for one bulb: \(4.50 \times 12 = \$54.00\).
- Find the total annual savings for 8 bulbs: \(54.00 \times 8 = \boxed{\$432}\), which corresponds to option B.
Explanation
- Analysis of the Electricity Savings Problem
We are tasked with determining the total annual electricity savings for replacing 8 incandescent bulbs with fluorescent bulbs. First, we identify the cost per hour and the monthly usage for each type of bulb. An incandescent bulb costs \(\$0.05\) per hour, and a fluorescent bulb costs \(\$0.02\) per hour. Each bulb is used for 150 hours per month. A year consists of 12 months. Our goal is to find the total money saved in a year for 8 bulbs.
- Calculating Monthly Savings per Bulb
We calculate the monthly cost of operating one incandescent bulb:
\[C_{I, monthly} = 0.05 \times 150 = \$7.50.\]
Next, we calculate the monthly cost of operating one fluorescent bulb:
\[C_{F, monthly} = 0.02 \times 150 = \$3.00.\]
The monthly savings for one bulb is the difference between these costs:
\[S_{monthly} = 7.50 - 3.00 = \$4.50.\]
- Calculating Annual Total Savings for Eight Bulbs
Now that we have the monthly savings per bulb, we calculate the annual savings for one bulb by multiplying by the 12 months in a year:
\[S_{annual, one} = 4.50 \times 12 = \$54.00.\]
Finally, we calculate the total annual savings for all 8 bulbs:
\[S_{total} = 54.00 \times 8 = \$432.00.\]
Comparing this result to the provided options, we see that it matches option b.
Examples
Understanding the cost-benefit analysis of energy-efficient appliances is essential in everyday life. For example, when choosing between different lighting options or electronic devices, calculating long-term savings helps in making financially responsible decisions. By evaluating the hourly energy consumption, you can estimate your household's annual savings, similar to how we calculated the savings for changing eight light bulbs: \(\$432\) per year. This simple math application helps individuals reduce their monthly bills and manage their resources effectively.