Answer :

mariangel
[tex] \frac{3}{2} = \frac{2x}{2x+y} [/tex]

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

[tex] \frac{2x+y}{2} = \frac{2x}{3} [/tex] = k

so we have:

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

x=[tex] \frac{3}{2} k[/tex]

[tex] \frac{x}{y} [/tex] = - [tex] \frac{3}{2} [/tex]

The corect answer is A. -3/2

or:

[tex] \frac{3}{2} = \frac{2x}{2x+y} [/tex]

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

[tex] \frac{2x+y}{2x} = \frac{2}{3} [/tex]

We use a property of proportions:

[tex] \frac{a}{b} = \frac{c}{d} [/tex]  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

[tex] \frac{a-b}{b} = \frac{c-d}{d} [/tex]  or

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

[tex] \frac{2x+y}{2x} = \frac{2}{3} [/tex]

[tex] \frac{(2x+y)-2x}{2x} = \frac{2-3}{3} [/tex]

[tex] \frac{y}{2x} = \frac{-1}{3} [/tex]

3y = - 2x

[tex] \frac{x}{y} = -\frac{3}{2} [/tex]



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