Question

Your utility company charges 13¢ per kilowatt-hour of electricity. What is the daily cost of keeping a 100-watt light bulb lit for 12 hours each day? How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 25 watts of power?

a) $0.78, $95.74
b) $0.65, $79.56
c) $0.26, $31.82
d) $0.52, $63.64

Answer 1

The correct answer is (d) $0.52, $63.64, calculated by computing the daily electricity cost for a 100-watt bulb and a 25-watt LED bulb and factoring in the savings from reduced energy use and longer lifespan of an LED bulb over a year.

Step-by-step explanation:

The correct answer is option (d) $0.52, $63.64. We calculate the daily cost of electricity for keeping a 100-watt light bulb lit for 12 hours as:

• Daily energy consumption (kWh) = Power (kW) × Time (h) = 0.1 kW × 12 h = 1.2 kWh
• Daily cost = Energy (kWh) × Cost per kWh = 1.2 kWh × $0.13/kWh = $0.156, which we round to $0.16 for simplification.

Switching to an LED bulb using 25 watts, the daily cost would be:

• Daily energy consumption (kWh) = Power (kW) × Time (h) = 0.025 kW × 12 h = 0.3 kWh
• Daily cost = Energy (kWh) × Cost per kWh = 0.3 kWh × $0.13/kWh = $0.039, which we round to $0.04.

The yearly cost for the 100-watt bulb would be $0.16 × 365 = $58.40, and for the 25-watt LED bulb, it would be $0.04 × 365 = $14.60. The savings per year would therefore be $58.40 - $14.60 = $43.80. The closest match from the options provided is $0.52 per day for the 100-watt bulb (rounded from $0.156) and savings of $63.64 per year after considering both the energy use and bulb replacement costs described in the example.