Question
Download Solution PDFIf x + y = 12, y + z = 15 and x + z = 18, then find x + y + z =?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
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