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high school simple algebra word problem

help please

New member
Sep 17, 2019
1
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?
 
Last edited:

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
644
I agree with your solution ... 200 hrs.
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,679
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.