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?
For an overlapping set problem we can use a double-set matrix to organize our information and solve. The boldfaced values were given in the question. The non-boldfaced values were derived using the fact that in a double-set matrix, the sum of the first two rows equals the third and the sum of the first two columns equals the third. The variable p was used for the total number of pink roses, so that the total number of pink and red roses could be solved using the additional information given in the question.
|TOTAL||100 — p||p||20||120|
The question states that the percentage of red roses that are short-stemmed is equal to the percentage of pink roses that are short stemmed, so we can set up the following proportion:
100 – p
5p = 1500 – 15p
p = 75
This means that there are a total of 75 pink roses and 25 red roses. Now we can fill out the rest of the double-set matrix:
Now we can answer the question. 20 of the 80 long-stemmed roses are red, or 20/80 = 25%.
The correct answer is B.