If the average (arithmetic mean) of x, y, and z is 7x and x...

Question

If the average (arithmetic mean) of x, y, and z is 7x and x is not equal to 0, what is the ratio of x to the sum of y and z ?

GMAT Panda · Accepted Answer

1:20 We first translate "average (arithmetic mean) of x, y, and z is 7x" into an equation. x+y+z/3 = 7x We multiply both sides by 3 and then subtract x from both sides to isolate y+z. x+y+z = 21x y+z = 21x - x y+z = 20x We then find the ratio of x to y+z by expressing x/y+z and simplifying the fraction. x/y+z = x/20x x/20x = xx20 1/20 ratio of x to y+z = 1:20

Explanation	Calculations	Help
$We first translate "average (arithmetic mean) of x, y, and z is 7x" into an equation.$	$\frac{x + y + z}{3} = 7 x$
$We multiply both sides by 3 and then subtract x from both sides to isolate y + z .$	$x + y + z = 21 x y + z = 21 x - x y + z = 20 x$
$We then find the ratio of to by expressing and simplifying the fraction.$	$\frac{x}{y + z} = \frac{x}{20 x} \frac{x}{20 x} = \frac{x}{x \times 20} \frac{1}{20} ratio of x to y + z = 1 : 20$

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