algebra addiltion problem

irene12

New member
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Dec 21, 2010
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15
Hello, I have an extra credit problem I would like to do, but I don't know where to start. Here it is :Find solution to 3/7=1/a+1/b+1/c where a, b, and c are positive intergers and a<b<c . Thank you. Any help would be great.
 

Denis

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Feb 17, 2004
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irene12 said:
Find solution to 3/7=1/a+1/b+1/c where a, b, and c are positive intergers and a<b<c .
1/a + 1/b + 1/c = 3/7 ; using LCD:
(bc + ac + ab) / abc = 3/7
Simplifying, in terms of c:
c = 7ab / (3ab - 7a - 7b)
At this point, you can tell that 3ab > 7a + 7b
Hope that "gets you going"...
For now: http://www.youtube.com/watch?v=nGd4jkaoHRg

EDIT: in case you're worried there might be no solutions, don't: there are 6 different solutions :idea:
 

soroban

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Jan 28, 2005
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Hello, irene12!

\(\displaystyle \text{Find solutions to: }\;\frac{1}{a} + \frac{1}{b} + \frac{1}{c}\:=\:\frac{3}{7}\; \text{ where }a, b, c\text{ are positive intergers and }a<b<c.\)

I found a number of solutions:

. . \(\displaystyle \frac{1}{3} + \frac{1}{12} + \frac{1}{84} \;=\;\frac{3}{7}\)

. . \(\displaystyle \frac{1}{3} + \frac{1}{11} + \frac{1}{231} \;=\;\frac{3}{7}\)

. . \(\displaystyle \frac{1}{3} + \frac{1}{14} + \frac{1}{42} \;=\;\frac{3}{7}\)

. . \(\displaystyle \frac{1}{3} + \frac{1}{15} + \frac{1}{35} \;=\;\frac{3}{7}\)


. . \(\displaystyle \frac{1}{4} + \frac{1}{6} + \frac{1}{84} \;=\;\frac{3}{7}\)

. . \(\displaystyle \frac{1}{4} + \frac{1}{7} + \frac{1}{28} \;=\;\frac{3}{7}\)


Do a Google search for "Egyptian fractions".

 

Denis

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Feb 17, 2004
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1,465
Soroban, I think you missed Irene's "an extra credit problem ";
I don't think we're allowed to give solution on these, only help.

Any other opinions?
 

irene12

New member
Joined
Dec 21, 2010
Messages
15
Thank you for the help with the problem. Both answers were very helpful because they both helped me solve the problem and hopefully, I will be able to solve this kind of problem on my own next time. With both answers, I can clearly see how and what to do. Thank you, Irene
 

mmm4444bot

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Staff member
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Oct 6, 2005
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10,251
Denis said:
Any other opinions?

My opinion is that soroban has already provided the regulars here with sufficient evidence to show that he doesn't care what we think.
 
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