how many pairs of positive integers m,n satisfy
1/m + 4/n = 1/12, given n is odd integer less than 60

op: 3,4,5,6,7

• 1/m + 4/n =1/12
  (n+4m)/mn =1/12
  12n+48m=mn
  12n=m(n-48)
  m=12n/(n-48)
  so, n= 49,51,53,55,57,59 and value of m should be an integer
  so by putting the values of n like 49,51,57........value of m will come integer so the answer is 3
  
• 9 years agoHelpfull: Yes(57) No(2)
• Actually this que was asked by one of the member but it was incomplete.
  
  solution is:-
  on solving above eq we get
  12n + 48m =mn
  mn - 12n - 48m = 0
  adding 576 both sides, we get
  mn - 12n - 48m + 576 =576
  (m-12)(n-48)=576
  since 576= 2^6*3^2
  now if n-48 is even then
  n=even+48 =even
  but we req to have n as odd
  so n-48 = odd
  now
  (n-48) * (m-12)= 2^6*3^2
  (n-48) * (m-12)= 1*(2^6*3^2),,,, [n-48=1] so [n=49]
  (n-48) * (m-12)= 3*(2^6*3),,,, [n-48=3] so [n=51]
  (n-48) * (m-12)= 9*(2^6*3^2),,,, [n-48=9] so [n=57]
  so there are 3 pairs of positive integers that satisfy the given eq with given conditions.
• 9 years agoHelpfull: Yes(12) No(4)
• 1/m+4/n=1/12
  m=12(n/n-48);
  hence n to be an odd integer there are 3 values to satisfy m is an integer
  n=49,51,57
  Apart from these values other odd ones are fraction.
  so possible pairs number is 3.
  
• 9 years agoHelpfull: Yes(2) No(0)
• 1/m+1/n=1/12
  or
  12n+48=mn
  or
  mn-12n-48m-576=576
  n(m-12)-48(m-12)=576
  (n-48)(m-12)=576
  if n is odd integer then n-48 will also be odd or rather an odd factor 576
  odd facors of 576 are 1,3,9
  so
  n-48=1 .... n=49(n
• 9 years agoHelpfull: Yes(0) No(1)
• 1/m=1/12-4/n,Since m is positive, n must be greater than 48. Possible odd values of n such that 48 < n < 60 are 49, 51, 53, 55, 57 and 59 of which only 49, 51 and 57 give integral values of m.
  For n=49,m= 588, n= 51,m=204 and n = 57, m=76. Ans-> Three pairs of +ve integers.
• 9 years agoHelpfull: Yes(0) No(0)
• Why is it taken odd integers..................... since the values satisfied between the range of 48
• 8 years agoHelpfull: Yes(0) No(0)