Question

What is the ratio of x to y?

Answer 1

$\frac{3}{2} = \frac{2x}{2x+y}$

From any proportion, we get another proportion by inverting the extremes (or the means):

$\frac{2x+y}{2} = \frac{2x}{3}$ = k

so we have:

2x=3k
2x+y=2k therefore:
3k+y=2k
y= - k

x=$\frac{3}{2} k$

$\frac{x}{y}$ = - $\frac{3}{2}$

The corect answer is A. -3/2

or:

$\frac{3}{2} = \frac{2x}{2x+y}$

From any proportion, we get another proportion by inverting the extremes and the means:

$\frac{2x+y}{2x} = \frac{2}{3}$

We use a property of proportions:

$\frac{a}{b} = \frac{c}{d}$  where a, d are extremes and b,c are means and the product of the extremes equals the product of the means (a*d=b*c),

so we have

$\frac{a-b}{b} = \frac{c-d}{d}$  or

$\frac{a+b}{b} = \frac{c+d}{d}$  (you can check this also by "the product of the extremes equals the product of the means")

$\frac{2x+y}{2x} = \frac{2}{3}$

$\frac{(2x+y)-2x}{2x} = \frac{2-3}{3}$

$\frac{y}{2x} = \frac{-1}{3}$

3y = - 2x

$\frac{x}{y} = -\frac{3}{2}$