MHB High school simple algebra word problem

AI Thread Summary
The discussion revolves around calculating the number of hours the 20W low energy bulb must be used to offset its higher initial cost compared to the 100W bulb. The initial assumption leads to a calculation of 200 hours, which is identified as a trap choice. The correct answer is stated as 160 hours, but participants express confusion over how to arrive at this figure. Clarification is sought on the reasoning behind the calculations, particularly regarding the exclusion of the initial cost of the 100W bulb. The conversation highlights the complexities of cost analysis in energy consumption and the importance of accurate equation formulation.
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The 100W light bulb (cost 0.60 dollars) is not going to be used anymore and is being replaced with the 20W (cost 3 dollars) low energy light bulb.
If electricity is charged at $0.15 per kWh, for how many hours must the low energy bulb be used in order for the lower cost of running it to exactly compensate for its higher initial cost?

A. 0.25
B 250.00
C 200.00
D 160.00
E 720.00

answer: D 160.00

why?

On first appearance you would think:
0.60 + 0.1 * 0.15 * t = 3.00 + 0.02 * 0.15 * t
t = 200

But that's the wrong answer. That's one of the trap choices.

How do you get to 160?

What am I misunderstanding or missing?
 
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I agree with your solution ... 200 hrs.
 
help please said:
The 100W light bulb (cost 0.60 dollars) is not going to be used anymore and is being replaced with the 20W (cost 3 dollars) low energy light bulb.
If electricity is charged at $0.15 per kWh, for how many hours must the low energy bulb be used in order for the lower cost of running it to exactly compensate for its higher initial cost?

A. 0.25
B 250.00
C 200.00
D 160.00
E 720.00

answer: D 160.00

why?

On first appearance you would think:
0.60 + 0.1 * 0.15 * t = 3.00 + 0.02 * 0.15 * t
t = 200

But that's the wrong answer. That's one of the trap choices.

How do you get to 160?

What am I misunderstanding or missing?
If you already have a 100W light bulb that is not going to be used anymore, then you don't need to spend $0.60 on a new one. So I would leave out the term 0.60 in the equation, which then becomes
0.1 * 0.15 * t = 3.00 + 0.02 * 0.15 * t.

But that leads to the answer t = 250. I don't see any way to get the answer 160 unless there is some further information that has been omitted from the question.
 
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