Question

If ab + b + a = 135 bc + b + c = 322 ca + a + c = 151 what is the value of a + b + c?

Answer 1

firstly take out values of a and b

then minus value of a from b

and then plus the given value of a with value of c

you will got yur answer

Answer 2

Answer:

Value of a + b + c is 28.

Step-by-step explanation:

Given:

ab + b + a = 135

bc + b + c = 322

ca + a + c = 151

To find: Value of  a + b + c

Consider,

ab + b + a = 135

ab + a + b + 1 = 135 + 1

( a + 1 )( b + 1 ) = 136 ............................(1)

bc + b +c = 47

bc + b + c + 1 = 47 + 1  

( b + 1 )( c + 1 ) = 48 ..............................(2)

Using (1) and (2)

(a+1)/(c+1)=17/6 ................................(3)

Also ,

ac + a + c = 101

ac + a + c + 1 = 101 + 1

( a + 1 )( c + 1 ) = 102 ..........................(4)

Using (3) and (4),

( a + 1 )( a + 1 ) = 17 × 17

So ,

( a + 1 ) = 17  ⇒ a = 17 - 1 = 16

( b + 1 ) = 8  ⇒ b = 8 - 1 = 7        ( from (1) )

( c + 1 ) = 6   ⇒ c = 6 - 1 = 5        ( from (3) )

So,

a + b + c = 16 + 7 + 5 = 28

Therefore, value of a + b + c is 28.