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Eighty percent of the lights at Hotel California are on at 8 [#permalink]
09 Sep 2008, 07:40

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? 22(2/9)% 16(2/3)% 11(1/9)% 10% 5%

My approach gets me --

Let T be the total number of light-bulbs, x = number that are supposed off y = number that are supposed on.

Then, y -0.1y +0.4x = 0.8T Also, x+y = T

Therefore, x = T/5 ...and 0.4x = 40% * (T/5) = 0.08T = 8%...what am I missing?

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? 22(2/9)% 16(2/3)% 11(1/9)% 10% 5%

My approach gets me --

Let T be the total number of light-bulbs, x = number that are supposed off y = number that are supposed on.

Then, y -0.1y +0.4x = 0.8T Also, x+y = T

Therefore, x = T/5 ...and 0.4x = 40% * (T/5) = 0.08T = 8%...what am I missing?

Say total 100 bulbs.

80 bulbs are on.

EDIT: sorry I forgot to add below calculations. x=bulbs that are supposed to be off y=bulbs that are supposed to be on

0.8(x+y) = 0.4x+0.9y y=4x x=20 y=80

40% of bulbs that suppose to be off actually on = 40/100 *20 =8

percent = 8/80 *100=10% _________________

Your attitude determines your altitude Smiling wins more friends than frowning

let the total no. of bulbs that are on be x........[B]

so total no. of bulbs = 5x/4 so bulbs actually off=5x/4 - x but given that actual bulbs that are off are 60% of the total no. of bulbs that were to be off. so total bulbs to be off = 10/6(5x/4-x). and it says out of total bulbs off, the no. of bulbs on are 40% so 0.4 *10/6*(5x/4 - x)..........[A] which is the total no. of bulbs that are on and which are to be off dividing A/B, we get .16666 or 16.66%.

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? 22(2/9)% 16(2/3)% 11(1/9)% 10% 5%

My approach gets me --

Let T be the total number of light-bulbs, x = number that are supposed off y = number that are supposed on.

Then, y -0.1y +0.4x = 0.8T Also, x+y = T

Therefore, x = T/5 ...and 0.4x = 40% * (T/5) = 0.08T = 8%...what am I missing? :(

You have got 0.4x that will be the fraction of total bulbs that are off. However, the question is asking the percentage of bulbs that are on and should be off. This will be 0.4x/0.8T.

I approached the question as below.

if f is the number of bulbs that should be off and n that should be on then. 0.4f + 0.9n = 0.8(f+n) => n = 4f.

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? 22(2/9)% 16(2/3)% 11(1/9)% 10% 5%

My approach gets me --

Let T be the total number of light-bulbs, x = number that are supposed off y = number that are supposed on.

Then, y -0.1y +0.4x = 0.8T Also, x+y = T

Therefore, x = T/5 ...and 0.4x = 40% * (T/5) = 0.08T = 8%...what am I missing? :(

You have got 0.4x that will be the fraction of total bulbs that are off. However, the question is asking the percentage of bulbs that are on and should be off. This will be 0.4x/0.8T.

I approached the question as below.

if f is the number of bulbs that should be off and n that should be on then. 0.4f + 0.9n = 0.8(f+n) => n = 4f.

I agree with the last post. That 20% bulbs are off does not mean that they are SUPPOSED to be off. The answer I am getting is 10% but with a different method. Let x = total no. of bulbs. Let N = On bulbs and Let F = off bulbs. N = 80x/100 and F = 20x/100 Since 40% bulbs that should be F(off) are N(on), 60% bulbs that should be F are ACTUALLY, F. In addition, 10% bulbs that should be N are F. Therefore, we get the equation for Off bulbs as follows: 60F/100 + 10N/100 = 20x/100 We know that x= N + F. Hence, 60F + 10(x-F)/100 = 20X/100. On solving, F/x = 1/5 This means, for every 100 bulbs, 80 are on. Also 40% of F are actually N i.e., 40/100 * 1/5 = 8% Therefore 8 out of 100 bulbs should be off but are on. The questioner wants to know what % of N is 8. We know that for every 100 bulbs, N = 80. Therefore, 8/80 = 10%.

I agree with the last post. That 20% bulbs are off does not mean that they are SUPPOSED to be off. The answer I am getting is 10% but with a different method. Let x = total no. of bulbs. Let N = On bulbs and Let F = off bulbs. N = 80x/100 and F = 20x/100 Since 40% bulbs that should be F(off) are N(on), 60% bulbs that should be F are ACTUALLY, F. In addition, 10% bulbs that should be N are F. Therefore, we get the equation for Off bulbs as follows: 60F/100 + 10N/100 = 20x/100 We know that x= N + F. Hence, 60F + 10(x-F)/100 = 20X/100. On solving, F/x = 1/5 This means, for every 100 bulbs, 80 are on. Also 40% of F are actually N i.e., 40/100 * 1/5 = 8% Therefore 8 out of 100 bulbs should be off but are on. The questioner wants to know what % of N is 8. We know that for every 100 bulbs, N = 80. Therefore, 8/80 = 10%.

GMBA85 and KASSALMD

Thanks for pointing out. I forgot to add the calculations. I edited the post now. _________________

Your attitude determines your altitude Smiling wins more friends than frowning

I agree with the last post. That 20% bulbs are off does not mean that they are SUPPOSED to be off. The answer I am getting is 10% but with a different method. Let x = total no. of bulbs. Let N = On bulbs and Let F = off bulbs. N = 80x/100 and F = 20x/100 Since 40% bulbs that should be F(off) are N(on), 60% bulbs that should be F are ACTUALLY, F. In addition, 10% bulbs that should be N are F. Therefore, we get the equation for Off bulbs as follows: 60F/100 + 10N/100 = 20x/100 We know that x= N + F. Hence, 60F + 10(x-F)/100 = 20X/100. On solving, F/x = 1/5 This means, for every 100 bulbs, 80 are on. Also 40% of F are actually N i.e., 40/100 * 1/5 = 8% Therefore 8 out of 100 bulbs should be off but are on. The questioner wants to know what % of N is 8. We know that for every 100 bulbs, N = 80. Therefore, 8/80 = 10%.

v well explained! good job! _________________

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