word problem

E

eric beans

Junior Member
Joined
Sep 17, 2019
Messages
72
The 100W light bulb (cost $.60) is not going to be used anymore and is being replaced with the 20W (cost $3) 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

why?

What am I misunderstanding here?
.02*.15*t = 3-.6
t= 800
 
eric beans said:
The 100W light bulb (cost $.60) is not going to be used anymore and is being replaced with the 20W (cost $3) 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

why?

What am I misunderstanding here?
.02*.15*t = 3-.6
t= 800
Click to expand...
Assume the costs are equal after 't' hours of use.

Cost of using incandescent bulb = 0.60 + 0.1 * 0.15 * t

Cost of using LED bulb = 3.00 + 0.02 * 0.15 * t

0.60 + 0.1 * 0.15 * t = 3.00 + 0.02 * 0.15 * t

3 - 0.60 = + 0.1 * 0.15 * t - 0.02 * 0.15 * t

Continue......
 
eric beans said:
The 100W light bulb (cost $.60) is not going to be used anymore and is being replaced with the 20W (cost $3) 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

why?

What am I misunderstanding here?
.02*.15*t = 3-.6
t= 800
Click to expand...
Your left-hand-side is the cost of electricity for the new bulb for t hours (with .02 being in kilowatts). The right-hand-side is the difference in cost of the bulbs. You have not accounted for the cost of electricity for the old bulb, which they apparently intend you to do, in order to compare cost with the new bulb with cost of continuing to run the old one. The question is slightly misleading on that.
 
Subhotosh Khan said:
Assume the costs are equal after 't' hours of use.

Cost of using incandescent bulb = 0.60 + 0.1 * 0.15 * t

Cost of using LED bulb = 3.00 + 0.02 * 0.15 * t

0.60 + 0.1 * 0.15 * t = 3.00 + 0.02 * 0.15 * t

3 - 0.60 = + 0.1 * 0.15 * t - 0.02 * 0.15 * t

Continue......
Click to expand...
2.4 = .015t-.003t
t = 200

still not 160.
 
Dr.Peterson said:
Your left-hand-side is the cost of electricity for the new bulb for t hours (with .02 being in kilowatts). The right-hand-side is the difference in cost of the bulbs. You have not accounted for the cost of electricity for the old bulb, which they apparently intend you to do, in order to compare cost with the new bulb with cost of continuing to run the old one. The question is slightly misleading on that.
Click to expand...
...but even when that is accounted for, it leads to 200, not 160 as the answer.

I'm still not sure why or how 160 has to be the right answer.
 
1) When I tried to work backwards, I plugged in 160 as 't' and multiplied it to cost of using new bulb, it gave $.48.
.02*.15*160 = $.48

I thought, how does $.48 fit into the rest of the problem? What could the significance of $.48 be? Could it be somehow $.60 (cost of old bulb) - $.12 (where would this figure come from?)

another angle I was thinking was:

2) If 200 is the "break even" point, curiously, choice 160 is 1) below the break even point and 2) is closest to break even point (difference of 40). How could this be used to explain the right answer? Are these observations alone significant enough to somehow make 160 the correct answer by process of elimination?
 
Last edited:
200 is a trap answer.

they knew many students would choose it. it's not the right answer though.
 
eric beans said:
2.4 = .015t-.003t
t = 200

still not 160.

200 is a trap answer.

they knew many students would choose it. it's not the right answer though.
Click to expand...
t=200 is the correct answer. You plugged in t=200 on side of the equation, now plug it into the other side. Then notice that you got the same answer so t=200 is correct.
 
You must log in or register to reply here.
Top