Question

if x ratio Y is equal to 2 ratio 3 find 3 X + 2 Y ratio 5 x + 3 y

Answer 1

Let x = 2k
and y = 3k

so, 3x+2y/5x+3y = 3(2k) +2(3k)/5(2k)+3(3k)
                            = 6k+6k/10k+9k = 12k/19k = 12:19

Answer 2

$let \: \frac{3x + 2y}{5x + 3y} = z \\ 3x + 2y = 5xz + 3yz \\ x(3 - 5z) = y(3z - 2) \\ \frac{x}{y} = \frac{3z - 2}{3 - 5z} \\ \frac{2}{3} = \frac{3z - 2}{3 - 5z} \\ 6 - 10z = 9z - 6 \\ 12 = 19z \\ z = \frac{12}{19}$