All the given options are correct
How to determine which of the equation is true?
The variation expression is given as
(2x + 3y) ∝ (x + 5y)
Rewrite as an equation
So, we have
(2x + 3y) = k(x + 5y)
Remove the brackets
So, we have
2x + 3y = kx + 5ky
Collect the like terms
So, we have
kx - 2x = 3y - 5ky
This gives
x(k - 2) = y(3 - 5k)
Divide by both sides by y(k - 2)
x/y = (5k - 3)/(2 - k) --- option (a)
Multiply both sides by y
x = y(5k - 3)/(2 - k) --- option (b)
Express x/y = (5k - 3)/(2 - k) as ratio
x : y = (5k - 3) : (2 - k) --- option (c)
Hence, all the given options are correct
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