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# Valentine Remains At the end of the day, February 14th, a

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Valentine Remains At the end of the day, February 14th, a [#permalink]

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27 Jan 2006, 09:44
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Valentine Remains
At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?

(A) 20%
(B) 25%
(C) 50%
(D) 75%
(E) 80%

THANKS
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Senior Manager
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27 Jan 2006, 10:12
(B) 25%

15/(15+x)=5/(5+y)
5+y+20+x+15=120

solve
n LS red roses = 20
20/80=25%

will explain more if needed
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27 Jan 2006, 10:43
Its B as explained. Was stuck for a few seconds on "The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed" once this idea was clear then it was a cake walk.
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Manager
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27 Jan 2006, 16:50
thanks
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09 Feb 2006, 13:50
The way I found it easiest is to just create a table

R W P Total
LS 20 0 60 80
SS 5 20 15 40
25 20 80 120

20/80 = 1/4 = 25%
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09 Feb 2006, 14:44
I B by creating a table, but it took me like 5 mins....
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09 Feb 2006, 18:24

We can write the equations:

R+P = 100 --(1)

15/p * 100% = 5/R * 100%
P = 3R --(2)

Substitute (2) to (1)
R = 25

# of long stemmed roses = 20
% of long stemmed roses = 20/25 * 100 = 80%
Attachments

working.xls [13.5 KiB]

working.xls [13.5 KiB]

Senior Manager
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10 Feb 2006, 09:45
Short Steam = (15W, 15P, 5R) = 40
Long Stem = (xP , yR) = 80

Now
15/(x+15) = 5/y+5

3y+15 = x+15
y/x = 1/3
y/(x+y) = 1/(3+1) =1/4 = 25% =Ans B
10 Feb 2006, 09:45
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