ab+a+b=250
bc+b+c=300
ca+a+c=216
find a+b+c??

• Answer is 45.25. Here is how I have done it. Please post any shortcut if available
  
  ab + a + b = 250
  a(1+b) + b = 250
  
  a = (250−b)(1+b)
  
  ac + a + c = 300
  c(1+a) + a = 300
  
  c = (300−a)(1+a)
  
  =300−(250−b)(1+b)1+(250−b)(1+b)=300(1+b)−(250−b)1+b+250−b
  
  =300(1+b)−(250−b)251=(50+301b)251=(50+301b)251
  
  bc + b + c = 216
  
  (50+301b)b251+b+(50+301b)251=216
  
  (50 + 301b)b + 251b + 50 + 301b = 54216
  
  301b2 +602b−54216 =0
  
  b=12.46
  
  a =(250−b)(1+b)=(250−12.46)(1+12.46) = 17.65
  c = (300−a)(1+a)=(300−17.65)(1+17.65) = 15.14
  
  These values of a,b and c statisfies the given conditions,as given below
  ab + a + b = 17.65 *12.46 + 17.65 + 12.46 ≈ 250
  ac + a + c = 17.65 *15.14 + 17.65 + 15.14 ≈ 300.21
  bc + b + c = 12.46 *15.14 + 12.46 + 15.14 ≈ 216
  
  Hence,
  a + b + c = 17.65 + 12.46 + 15.14 = 45.25
• 11 years agoHelpfull: Yes(4) No(6)
• ans 68
  ab+a+b=250 ....1
  bc+b+c=300 ....2
  ca+a+c=216 ....3
  
  multiply eq 1 by c, eq 2 by a and eq 3 by b
  now solve 1 & 2, b=-50
  2&3,c=84
  3&1,a=34
  34-50+84=68
• 11 years agoHelpfull: Yes(3) No(17)
• sorry i did a mistake in my soln, the ans will be 45
• 11 years agoHelpfull: Yes(3) No(3)
• pls tell what r the option...more then 1 option r possible...thats why i asked..i got 3 ans....
• 11 years agoHelpfull: Yes(1) No(2)
• Add 1 on both sides
  ab+a+b+1=251==>(a+1)(b+1)=251--->1
  bc+b+c+1=301==>(b+1)(c+1)=301--->2
  ca+a+c+1=217==>(c+1)(a+1)=217--->3
  Divide 1 by 2
  (a+1)/(c+1)=0.83388==(a+1)=0.83388(c+1)--->4
  from 3 (a+1)(c+1)=217, substitute 4 in 3
  c=15.1315
  by solving we get b=17.6590, a=12.4519
  a+b+c=12.4519+17.6590+15.1315==45.24
• 9 years agoHelpfull: Yes(1) No(0)
• 2(ab+bc+ca)+2(a+b+c)=766
  2(250-a-b+300-b-c+216-a-c)+2(a+b+c)=766
  1532-(a+b+c)=766
  2(a+b+c)=766
  a+b+c=383
• 6 years agoHelpfull: Yes(1) No(1)
• jusr replace a by b b by c and reduce the eqtns a one variable stmnt
  
• 11 years agoHelpfull: Yes(0) No(1)
• i feel data is insufficient.can any 1 give me the solution with all steps????
• 11 years agoHelpfull: Yes(0) No(2)
• a=34;
  b=-50;
  c=84;
  a+b+c=68
• 11 years agoHelpfull: Yes(0) No(4)
• Answer is 45.25
• 10 years agoHelpfull: Yes(0) No(0)