Question

If a : b = 5 : 3, show that (5a + 8b) : (6a – 7b) = 49 : 9.

Answer 1

Given a : b = 5 : 3
⇒ `a/b = (5)/(3)`
∴ `(5a + 8b)/(6a - 7b) = (5(a/b) +8)/(6(a/b)-7)`
Numberator and Denominator is divided by 'b'.
= `(5 xx 5/3 + 8)/(6 xx 5/3 -7)`
= `(49)/(9)`
= 49 : 9.
Hence proved.