(y+3):(y+5)=k:1 show that y=(5k-3)/(1-k)

Question

(y+3):(y+5)=k:1
show that y=
`(5k-3)/(1-k)`

Answer 1

see explanation

Explanation:

Express the ratios in fractional form, that is

`(y+3)/(y+5)` =
`(k)/(1)` ( cross- multiply )

y + 3 = k(y + 5) ← distribute

y + 3 = ky + 5k ( subtract ky from both sides )

y - ky + 3 = 5k ( subtract 3 from both sides )

y - ky = 5k - 3 ← factor out y from each term on the left side

y(1 - k) = 5k - 3 ← divide both sides by (1 - k)

y =
`(5k-3)/(1-k)`