Math Olympiad | A Nice Rational Equation | 90% Failed to solve!

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#rational #matholympiad #maths #rationalequations

[adamrussell]

1 factor all denominators
2 count how many of each prime is required, multiply to find least common denominator = 45045
3 divide LCD by each initial denominator to find the numerators 15025, 3003, 1287, 715, 455, 315
4 sum to find numerator = 20790
5 result is 20790*M/45045 = 48
M = 48*45045/20790 = 104

[Nazimİsmayılov-eu]

mötərizələri açıb əks ədədləri islah etdikdən sonra
m/2(1-1/13)=48
m/2×12/13=48
m×12/2×13=48
m×6/13=48
m=48÷6/13=48×13/6=8×13=104

[ManojkantSamal]

(m/2)× {1-(1/13)}=48
(m/2)×(12/13)=48
(m/2)=(48×13)/12=52
m=52×2=104

[key_board_x]

(m/3) + (m/15) + (m/35) + (m/63) + (m/99) + (m/143) = 48
(m/3) + [(m/3) * (1/5)] + [(m/7) * (1/5)] + [(m/7) * (1/9)] + [(m/11) * (1/9)] + [(m/11) * (1/13)] = 48
(m/3).[1 + (1/5)] + (m/7).[(1/5) + (1/9)] + (m/11).[(1/9) + (1/13)] = 48
(m/3).[(5/5) + (1/5)] + (m/7).[(9/45) + (5/45)] + (m/11).[(13/117) + (9/117)] = 48
[(m/3) * (6/5)] + [(m/7) * (14/45)] + [(m/11) * (22/117)] = 48
[m * (2/5)] + [m * (2/45)] + [m * (2/117)] = 48
m * [(2/5) + (2/45) + (2/117)] = 48
m * [(1/5) + (1/45) + (1/117)] = 24
m * [(9/45) + (1/45) + (1/117)] = 24
m * [(10/45) + (1/117)] = 24
m * [(2/9) + (1/117)] = 24 → recall: 117 = 9 * 13
m * [(1/9).(2) + (1/9).(1/13)] = 24
m * (1/9) * [2 + (1/13)] = 24
m * (1/9) * [(26/13) + (1/13)] = 24
m * (1/9) * (27/13) = 24
m * (27/9) * (1/13) = 24
m * 3 * (1/13) = 24
m * (1/13) = 8
m = 13 * 8
m = 104

[tensor]

despite being familiar with the key result I missed it and just cleared the fractions (getting me nowhere) ... groan!!!!

[larrydickenson]

I don’t understand a single thing this guy did.

[EshAnian-qo]

See this is not the way to teach. How does one realise that one should do 1/a-1/b. For different series different such formulae must be used. Unless you have solved this exercise previously you can use the 1/a-1/b. This is rote learning.

This is the problem with Indian education. We don’t teach how the different formulae have to be used for different situations.

This is an extremely poor teaching and our nonsense.

[EshAnian-qo]

Why are you teaching in Hindi? Teach in English.

[EshAnian-qo]

See this is not the way to teach. How does one realise that one should do 1/a-1/b. For different series different such formulae must be used. Unless you have solved this exercise previously you can use the 1/a-1/b. This is rote learning.

This is the problem with Indian education. We don’t teach how the different formulae have to be used for different situations.

This is an extremely poor teaching and our nonsense.