Question

If `a/b = c/d` then prove that each of the given ratio is equal to `(3a + 2c)/(3b + 2d)`.

Answer 1

Let `a/b = c/d` = k

a = bk

c = dk

`(3a + 2c)/(3b + 2d) = (3(bk) + 2(dk))/(3b + 2d)`

= `(k(3b + 2d))/(3b + 2d)`

= k

Since we established that the original ratios `a/b and c/d` both equal k, and the new ratio `(3a + 2c)/(3b + 2d)` also equals k they are all equal to each other:

`a/b = c/d = (3a + 2c)/(3b + 2d)`