Question 1179662: Divide 75 into two parts so that one part is 2/3 of the other.
Found 4 solutions by MathLover1, mananth, ikleyn, n2: Answer by MathLover1(20855) (Show Source): Answer by mananth(16949) (Show Source): Answer by ikleyn(53725) (Show Source):
You can put this solution on YOUR website! .
Divide 75 into two parts so that one part is 2/3 of the other.
~~~~~~~~~~~~~~~~~~~~~~~
Calculations in the post by @mananth are incorrect.
I came to bring a correct solution.
If one part is x
the other part will be 2x/3
x+ 2x/3 =75
(3x+2x)/3=75
5x = 225
x = 45
You can find the other part
2/3 x = 2/3 * 45 = 30.
ANSWER. The parts are 45 cm and 30 cm.
Solved correctly.
Answer by n2(76) (Show Source):
You can put this solution on YOUR website! .
It is my cumulative review #2 to solutions by @mananth at this forum.
For my previous cumulative review #1 see the link
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1130236.html
From Jan.9, 20026 and during Jan. 2026 I continued checking solutions
provided by @mananth at this forum www.algebra.com .
For now, Feb.03, 2026, I reviewed/checked about 2*17*31 = 1054 problems, solved
by @mananth at this web-site (problems from 0..29 to 1260..1289 inclusively
of the list https://www.algebra.com/tutors/your-answers.mpl?userid=mananth ).
Of them, I found about 83 problems solved incorrectly.
Below is the list of these problems, solved incorrectly.
For each of these problems, my correct solution is placed at the same spot/link.
I started this my checking job from some of the problems, and after checking approximately 70 problems,
I started noticing the repeating patterns in problems and in their solutions.
Quite often, these solutions were incorrect, and the errors were of the kind a live person would not
make them. It led me to the idea that the solution were actually produced not by a living person,
but by a computer code, instead. So, it was a very early version of the Artificial Intelligence.
After getting this observation, two ideas led me.
First idea was, of course, to clean this forum from erroneous solutions.
Second idea was to learn how far this artificial intelligence may lead in producing wrong and right solution.
So, this file is my report on this issue.
I collected here only wrong solutions (wrong from a Math point of view).
There were also cases, when the solutions were led to correct answers, but were wrong
from an educative/pedagogical point of view. Then suggestions "wrong/correct" become more individualized/personalized,
and I did not include such cases in this my file. So, only incorrect solutions are collected/listed here.
From about 1000 reviewed problems, the number of incorrectly solved is about 80 (for now).
In other words, about 8% of all problems were solved incorrectly by @mananth (by his version of AI).
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1186851
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Finance/1201799: M wishes to determine how long it will take an initial deposit of $10,000 to double.
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c) Reviewing your findings in parts a and b, indicate what relationship exists between the interest rate
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Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.)
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1182271
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1179655
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1179662
Divide 75 into two parts so that one part is 2/3 of the other.
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1179401
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1053994 (80)
If Jackson deposited $400 at the end of each month in the saving account earing interest at the rate of 6%/year compounded monthly,
how much will he have on deposite in his savings account at the end of 6 years, assuming that he makes no withdrawals during that
period? Round your answers to two decimal places.
https://www.algebra.com/algebra/homework/expressions/expressions.faq.question.1053994.html
1198831
If a bank pays 15% compounded semi-annually, how much should be deposited now to have $1800 in 5 years from now?
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1198831.html
1180616
pilot heads his jet due east. The jet has a speed of 680 km/h relative to the air. The wind is blowing due north with a speed of 64 km/h
Find the true speed and direction of the jet
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1180616.html
1179966 (83)
Ellis is painting wooden fenceposts before putting them in his yard. They are each 5 feet tall and have a diameter of 1 foot.
There are 10 fenceposts in all. How much paint will Ellis need to paint all the surfaces of the 10 fenceposts? Use 3.14 for π,
and round your answer to the nearest hundredth.
https://www.algebra.com/algebra/homework/formulas/Geometric_formulas.faq.question.1179966.html
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You may ask me - ok, @mananth is a computer code, or AI - what does it change ?
Ok, below are my thoughts and my suggestions about it.
(1) First, 8.3% wrong solutions is too much for an AI.
You may say "ok, in 20 years it will be perfect".
Probably, it can be true, but I tell you about what I see now.
By the way, my feeling is that good AI acceptable level for wrong solutions
should be at most 1:1000, or 0.1%.
(2) Second, it can be perfect in 20 years under one necessary condition:
the best minds in Math solving, writing and teaching, the best Math educators
and the best computer programming specialists will work on it
starting from now and during 20 years.
What does it mean and why ? - Raising and educating a specialist in solving Math, writing Math
and explaining Math takes 10 - 15 - 20 years to get a professional level, when a person can speak,
write and teach professionally. (And, usually, the fingers of one hand are enough
to count such specialists of a national level in each country and in each generation).
If you make such experiments with the novices, it will take 10-15-20 years for them to get a professional
level before they will learn to speak/write at the professional level, so it is a WRONG way to assign
novices for key positions for such an activity.
It is the second conclusion from my arguments: the writers and the content creators must be professionals
from the very beginning. Neither @mananth, nor @CPhill are such professionals.
(3) Third, when a computer code (like Artificial Intelligence) produces wrong solutions, it becomes
double and triple dangerous, since it works as the source of unlimited erroneous solutions.
So, such pretendent to the AI position is needed in doubled and tripled attention from developers,
from well-wishers around and from the whole community.
Often, I see the solutions by @mananth (= or his code) that produce correct final answer,
but are incorrect from the point of view of the teaching methodology.
When a computer code (like Artificial Intelligence) produces pedagogically wrong solutions,
then such tools become inappropriate for teaching - and again, they require doubled and tripled attention.
(4) Fourth, the computer codes which I see in the posts by @CPhill or @mananth, have no that level of flexibility
and precision to serve at the adequate level. So, the level of the computer coders must be at least
one order (one level) higher.
(5) Fifth, the writing, coding and programming discipline must be changed.
For now, the AI codes for solving school Math problems that I saw so far, do not show a tendency
to make checks of their solutions. They do not think that is is MANDATORY. It is a crude error,
which must be fixed.
(6) Next. As the life has taught me, many of incoming problems are mathematically non-sensical.
So, the input flow is quite dirty, and therefore, idiotic incoming problems should be filtered out.
OK. So, these are conclusions and directions from my overview that should be taken into account by developers of AI,
if they want to have a perfect product in 20 years.
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
OK and very good.
There is one more issue, which I hesitate to pronounce.
It is well known fact that the peak in school Math education in the world (in all industrially
developed countries) was from the middle of 1950s to, roughly say, 1970.
After that peak, the recession of the level of Math education was observed worldwide.
So and therefore, the specialists who are able to communicate with young students,
to speak with them, to teach them Math, to inspire them and who got their Math education at that time,
have a special value. People of this generation are quite old and will go out soon -
so and therefore, it is of great importance, great necessity and high urgency to use the experience
of those of them, who still have a potential to share their knowledge, skills, style, tone, spirit and abilities.
When these people will go out totally, it will be too late.
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