\(\frac{3}{2} = \frac{2x}{2x+y}\)
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 (ad=bc),
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
\(\frac{x}{y} = -\frac{3}{2}\)
