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Question 1210704: Frank has a festoon which he lights up for the village festa.
The festoon has white and blue bulbs in the ratio 3:5. It has 45 white bulbs.
This year, he wants to change the ratio of white and blue bulbs in the festoon to the
ratio of 1:3. He will keep the same total number of bulbs in his festoon.
How many more blue bulbs will there be in this year’s festoon?
Found 4 solutions by ikleyn, math_tutor2020, greenestamps, MathTherapy:
Answer by ikleyn(54017)   (Show Source):
You can put this solution on YOUR website! .
Frank has a festoon which he lights up for the village festa.
The festoon has white and blue bulbs in the ratio 3:5. It has 45 white bulbs.
This year, he wants to change the ratio of white and blue bulbs in the festoon to the
ratio of 1:3. He will keep the same total number of bulbs in his festoon.
How many more blue bulbs will there be in this year’s festoon?
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It can be solved using equations or mentally, without using equations.
Since the problem does not provide instructions on which method to use,
I will choose the simplest way: a mental solution.
Originally, Frank has 45 white bulbs that represent 3 equal parts.
Hence, one/each equal part is 45/3 = 15 bulbs.
So, the number of blue bulbs Frank originally has is 5*15 = 75.
Thus, the total number of bulbs Frank has is 45 + 75 = 120.
Now Frank wants to have these 120 bulbs in the proportion white : blue = 1:3.
So, 120 bulbs should be divided into 1 + 3 = 4 equal parts.
Hence, one/each such part must have 120/4 = 30 bulbs.
This gives 30 white bulbs and 30*3 = 90 blue bulbs.
So, this year Frank's festoon will have 90-30 = 60 more blue bulbs than white bulbs. ANSWER
Solved.
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Tutor @greenstamps noted that the problem, as given in the post, allows for different interpretations.
It is a very important observation.
True Math problems do not allow different interpretations.
This my comment goes to the person who initiated/created/composed/translated this problem,
and to future readers of this post.
The problem, as given in the post, is defective and can not be considered a true Math problem.
I insist on this because school math problems—and mathematics in general—are not merely exercises
in problem-solving techniques; they are also an important educational tool that teaches a person to distinguish
truth and precise statements from falsehoods or half-truths.
Thanks to tutor @Greenestamps (!)
Answer by math_tutor2020(3847)  (Show Source):
You can put this solution on YOUR website!
Answer: 60
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Explanation
I'll use last year's ratio to find how many blue bulbs there were.
white/blue = 3/5
45/b = 3/5
45*5 = 3b
b = 45*5/3
b = 75
Last year he had 45 white bulbs and 75 blue bulbs.
That yields a total of 45+75 = 120 bulbs.
I'll let the student confirm that the ratio 45:75 reduces to 3:5
Note the GCF of 45 and 75 is 15.
This year Frank wants the white:blue ratio to be 1:3
w = number of white this year
3w = number of blue this year
The ratio w:3w reduces to 1:3 after dividing both parts by w.
The pieces w and 3w need to add to the previous total (120) since Frank will "keep the same total number of bulbs in his festoon".
w+3w = 120
4w = 120
w = 120/4
w = 30
This year he'll need 30 white bulbs and 3w = 3*30 = 90 blue bulbs.
blue - white = 90-30 = 60 more blue bulbs are needed in comparison to white bulbs.
Or once you determine w, you can do the following:
blue - white = (3w) - (w) = 2w = 2*30 = 60
Answer by greenestamps(13380)  (Show Source):
You can put this solution on YOUR website!
"How many more blue bulbs will there be in this year’s festoon?"
There are two distinctly different interpretations of that question.
Both of the tutors who responded so far have interpreted the question to be asking how many more blue bulbs are there than white bulbs in this year's festoon.
To me, the grammatically more reasonable interpretation is that the question is asking how many more blue bulbs there are in this year's festoon than in last year's festoon.
The numbers in the responses from the other tutors are all correct; but now if we are interpreting the question differently the answer is different.
Both years the total number of bulbs was 120. Last year the ratio of white to blue bulbs was 3:5, giving 45 white and 75 blue. This year that ratio is 1:3, giving 30 white and 90 blue.
So this year there are 90-75 = 15 more blue bulbs than last year.
ANSWER: 15
Answer by MathTherapy(10864)  (Show Source):
You can put this solution on YOUR website!
Frank has a festoon which he lights up for the village festa.
The festoon has white and blue bulbs in the ratio 3:5. It has 45 white bulbs.
This year, he wants to change the ratio of white and blue bulbs in the festoon to the
ratio of 1:3. He will keep the same total number of bulbs in his festoon.
How many more blue bulbs will there be in this year’s festoon?
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Yes, the question asked is quite VAGUE!
Last year: White to Blue: 3:5 = 45:75. Total: 45 + 75 = 120
This year: White to Blue: 1:3 = 30:90 Total: 30 + 90 = 120
Answer # 1: How many more blue balls, this year, than blue balls, last year? 90 - 75 = 15
Answer # 2: How many more BLUE balls, this year, than WHITE balls? 90 - 30 = 60
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