Question

What is the ratio of x to y?

3/2=2x/2x+y

A. -3/2

B. -2/3

C. 2/3

D. 3/2

Answer 1

`(3)/(2) = (2x)/(2x+y)`

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


`(2x+y)/(2) = (2x)/(3)` = k

so we have:

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

x=
`(3)/(2) k`


`(x)/(y)` = -
`(3)/(2)`

The corect answer is A. -3/2

or:


`(3)/(2) = (2x)/(2x+y)`

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


`(2x+y)/(2x) = (2)/(3)`

We use a property of proportions:


`(a)/(b) = (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


`(a-b)/(b) = (c-d)/(d)` or


`(a+b)/(b) = (c+d)/(d)` (you can check this also by "the product of the extremes equals the product of the means")


`(2x+y)/(2x) = (2)/(3)`


`((2x+y)-2x)/(2x) = (2-3)/(3)`


`(y)/(2x) = (-1)/(3)`

3y = - 2x


`(x)/(y) = -(3)/(2)`