Solve this simple problem 'Simply'

Algebra Level 2

If, $\frac{x+y}{2}=\frac{y+z}{3}=\frac{z+x}{4}$ Then $x:y:z$ can be expressed as a:b:c where $a, b$ & $c$ are positive co-prime integers. What's $a+b+c$ ? ( $x, y, z$ are positive reals.)

The answer is 9.

1 solution

Sanjeet Raria
Sep 6, 2014

Here's the 'Simple' solution-

$Each Ratio =\frac{\textit {Sum of the Numerators}}{\textit {Sum of the Denominators}}=\frac{2(x+y+z)}{9}=\frac{(x+y+z)}{9/2}$ $=\frac{(x+y+z)-(y+z)}{\frac{9}{2}-3}=\frac{(x+y+z)-(x+z)}{\frac{9}{2}-4}=\frac{(x+y+z)-(x+y)}{\frac{9}{2}-2}$ $=\frac{x}{3/2}=\frac{y}{1/2}=\frac{z}{5/2}$ $=> x:y:z=3:1:5$ Ans. $\boxed9$

Solve this simple problem 'Simply'

The answer is 9.

1 solution

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