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If ab + b + a = 135 bc + b + c = 47
ca + a + c = 101
What is the value of a + b + c?
Read Solution (Total 3)
-
- ab+a+b+1 = 135 + 1
a(b+1)+1(b+1) =136
(a+1)(b+1) =136 —-1
Same for further 2
(b+1)(c+1)=48 ——2
(a+1)(c+1)=102 ——-3
Now make factors
For eq1 , factors 17*8
For 2, factors 8*6
For 3 , factors 6*17
So by factors
a+1 = 17
a=16
b+1=8
b=7
c+1=6
c=5
a+b+c=28 - 6 years agoHelpfull: Yes(18) No(1)
- 2(ab+bc+ca)+2(a+b+c)=283
2(135-a-b+47-b-c+101-a-c)+2(a+b+c)=283
566-(a+b+c)=283
2(a+b+c)=283
a+b+c=141.5 - 6 years agoHelpfull: Yes(2) No(24)
- ab+a+b=135 -----(1)
bc+b+c=47 -----(2)
ca+b+c=101 -----(3)
1st step:
take equation 1 and add 1 on both sides
ab+a+b+1=135+1
a(b+1)+b+1=136
b+1(a+1)=136 -------(4)
take equation (2) and add 1 on both sides
bc+b+c +1=47+1
b(c+1)+c+1=48
c+1(b+1)=48 ---------(5)
take equation (3) & add 1 on both sides
ca+a+c+1=101+1
a(c+1)+c+1=102
c+1(a+1)=102 ---------(6)
solve using this 4*5/6
((b+1)(a+1))*((c+1)(b+1))/((c+1)(a+1))=138*48/(102)
eliminate and solve
(b+1)^2=6528/102
=64
b+1=root(64)
b+1=8
b=7 --------(7)
use b=7 in (4)
(7+1)(a+1)=136
8a=136-8
8a=128
a=128/8=16
a=16 ----------------------(8)
sub b=7 in(5)
(c+1)(7+1)=48
8c=48-8
c=40/8=5
c=5 ------------(9)
therefore (7)+(8)+(9)=16+7+5=28
ANSWER: a+b+c=28 - 3 years agoHelpfull: Yes(0) No(0)
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