If x + y = 12, y + z = 15 and x + z = 18, then find x + y + z =?

Question

Question

Answer 1

Given:

x + y = 12, y + z = 15, x + z = 18

Calculation:

x + y = 12 ----(1)

y + z = 15 ----(2)

x + z = 18 ----(3)

By solving equations (1) and (2)

⇒ x – z = -3 ----(4)

By solving equations (3) and (4)

⇒ x = 7.5

Put the value of x in equation (1)

⇒ y = 4.5

Put the value of y in equation (2)

⇒ z = 10.5

x + y + z

⇒ 7.5 + 4.5 + 10.5

⇒ 22.5

∴ The value of x + y + z is 22.5.

Shortcut Trick

Add (1), (2) and (3)

⇒ 2(x + y + z) = 45

⇒ (x + y + z) = 45/2 = 22.5

∴ The value of x + y + z is 22.5.