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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.
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.
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