Question

If `x/(a + b - c) = y/(b + c - a) = z/(c + a - b) = 5` and a + b + c = 7; the value of x + y + z is ______.

Options

• 35

• `7/5`

• `5/7`

• 42

Answer 1

If `x/(a + b - c) = y/(b + c - a) = z/(c + a - b) = 5` and a + b + c = 7; the value of x + y + z is 35.

Explanation:

Given

`x/(a + b - c) = y/(b + c - a) = z/(c + a - b) = 5`

∴ Each fraction

= `(x + y + z)/(a + b - c + b + c - a + c + a - b)`

`\implies (x + y + z)/(a + b + c) = 5`

`\implies (x + y + z)/7 = 5`  ...[Given a + b + c = 7]

`\implies` x + y + z = 35