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?

25%.

Step-by-step explanation:

We have been given that 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.

We are also told that 1/3 of the roses were short-stemmed.

Since 20 of those were white and 15 of which were pink, so short stemmed red roses would be .

Now, we will find number of long-stemmed roses by subtracting number of short-stemmed roses from total roses as:

We are also told that none of the long-stemmed roses were white, so total number of white roses would be .

Let p represent the number of total pink roses.

Now, total number of red roses would be total roses (120) minus total pink roses (p) minus total white roses (20).

We have been given that the percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. We can represent this information in an equation as:

Let us solve for p by cross-multiplication:

Since total number of pink roses is 75, so total number of red roses would be .

We already figured it out that 5 roses are short-stemmed, so long-stemmed roses would be .

Now, we have long stemmed roses is equal to 20 and total long-stemmed roses is equal to 80.

Let us find 20 is what percent of 80.

Therefore, 25% of the long-stemmed roses were red.