proportion

if a/b = c/d = e/f
then show that these ratios are equal to 
(5a - 7c + 3e) / (5b -7d + 3f)



Answer:

let  a/b = c/d = e/f = k
therefore, a = bk, c = dk and e = fk
substituting in  (5a - 7c + 3e)
we get, 5bk - 7dk + 3fk  = k(5b - 7d + 3f)

Therefore,
(5a - 7c + 3e) / (5b -7d + 3f) = k(5b -7d + 3f) / (5b -7d + 3f) = k
Hence (5a - 7c + 3e) / (5b -7d + 3f)  has same value as the ratios.

If p/q = r/s = t/u, then prove that (p² – pr +t²)/(q² – qs + u²) = pt/qu

Answer

let,  p/q = r/s = t/u = k

so, p = qk, r = sk and t = uk

therefore, (p² – pr +t²) = q²k² - qsk² - u²k² = k²(q² - qs - u²)

therefore, (p² – pr +t²)/(q² – qs + u²) = k²(q² - qs - u²)/ (q² - qs - u²) = k²

= p/q x t/u

= pt/qu