Eco-Friendly Light Bulb Dilemma

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Alex is considering switching to LED light bulbs for his home to save energy and money in the long run. He has two options:

1. Traditional incandescent bulbs: A pack of 4 costs $3, and each bulb lasts about 1,000 hours.
2. LED bulbs: A single bulb costs $8 and lasts about 25,000 hours.

Assume that Alex uses the light bulb for an average of 5 hours per day.

Questions

a) How many days will a single incandescent bulb last?

b) How many days will the LED bulb last?

c) After how many days will the LED bulb become more cost-effective than buying incandescent bulbs?

Round all answers to the nearest whole number.

# Eco-Friendly Light Bulb Dilemma: Solution a) Days a single incandescent bulb lasts: – Hours per day: 5 – Bulb lifespan: 1,000 hours – Days = 1,000 ÷ 5 = 200 days b) Days the LED bulb lasts: – Hours per day: 5 – Bulb lifespan: 25,000 hours – Days = 25,000 ÷ 5 = 5,000 days c) Days until LED becomes more cost-effective: Let’s create a table to compare costs over time:

Days	Incandescent Cost	LED Cost
200	$0.75	$8.00
400	$1.50	$8.00
600	$2.25	$8.00
800	$3.00	$8.00
1000	$3.75	$8.00
1200	$4.50	$8.00
1400	$5.25	$8.00
1600	$6.00	$8.00
1800	$6.75	$8.00
2000	$7.50	$8.00
2200	$8.25	$8.00

The LED bulb becomes more cost-effective after 2,134 days (rounded to the nearest whole number). Calculation: – Cost per day for incandescent: $0.75 ÷ 200 = $0.00375 – Days until costs equal: $8 ÷ $0.00375 = 2,133.33 – Rounding up: 2,134 days Therefore, after 2,134 days (about 5 years and 10 months), the LED bulb becomes more cost-effective than buying incandescent bulbs.