Find the value of x + y + z, if x + y + xy = 3, y + z + yz = 8, x + z + xz = 15.

A. 53/6

B. 49/6

C. 43/6

D. 57/6

Detailed Solution: 

The correct answer is 43/6

x + y + xy = 3

Adding 1 on both sides of the equation

we get,

! + x + y + xy = 4

⇒ (1+x) + y(1+x) = 4

⇒ (!+x) (1+y) = 4  --------------(1)

Similarly on other 2 equations, 

y + z + yz = 8

⇒ 1 + y + z + yz = 9

⇒ (1+ y) + z(1 +y) = 9

⇒ (1 + y) (1 + z) = 9  -------------(2)

x + z + xz = 15

⇒  1 + x + z + xz = 16

⇒ (1+ x) + z(1 +x) = 16

⇒ (1+ x) (1+ z) = 16 -------------(3)

Multiplying equations (1), (2) and (3)

⇒ [ (1 + x) (1 + y) (1 + z) ]²    

⇒ ( 4 x 9 x 16 )

⇒  [ (1 + x) (1 + y) (1 + z) ] = [ 2 x 3 x 5 ] ---------(4)

From equation (1) and (4)

⇒ (1 + z) = 6

⇒ z = 5

Similarly, from equation (2) and (4)

(1 + x) = 8/3

x = 5 / 3

Similarly, from equation (3) and (4)

(1 + y) = 3/2

y = 1/2

∴ x + y + z = 5/3 + 1/2 + 5 = 43/6.