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Word Problem - Percent

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Word Problem - Percent

by jnellaz » Mon Nov 10, 2008 11:58 am
Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?

a) 22(2/9)%
b) 16(2/3)%
c) 11(1/9)%
d) 10%
e) 5%

[spoiler]The answer is: D[/spoiler][spoiler]

I read a solution for this question that was a bit hard for me to follow. Can anyone provide any pointers on a problem like this? Thanks
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by cramya » Mon Nov 10, 2008 2:24 pm
I dont know if there are any pointers but hope this helps. Let me know if u still have any questions.

Let T be the total number of lights i.e since problem involves percents let T=100

80%of the lights are on currently i.e 80 lights are on

Let x be the lights that are usually off
Let y be the lights that are usually on

x+y =100 (1)

forty percent of the lights that are supposed to be off are actually on = .40x

ten percent of the lights that are supposed to be on are actually off = .10y

So the number of lights on = forty percent of the lights that are supposed to be off are actually on + 90% of the lights that are usually on
80 = .40x + .90y

i.e 4x+9y=80 (2)

From 1) and 2) x=20(40%OF THIS IS 8) y =80(90%OF THIS IS 72)

(72+8 = 80 gives us the lights taht are on currently)

Percent of the lights that are ON but are supposed to be OFF
= 8/80*100 = 10%

D)
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