South Korean Ratio Question

[milanproda]

The ratio of South Korean aircraft to North Korean aircraft was 1 to 3. After the North announced it would acquire nuclear weapons, the US sent 60 aircraft to South Korea. Then, the ratio became 3 to 5. What was the total number aircraft on the Korean Peninsula after the US aircraft transfer?

a- 120
b- 135
c-225
d-300
e-360 (answer)

I spent 45 minutes on this and I cant crack it =(

[N:Dure]

Before the US got in, the ratio of S:N was 1:3 i.e 3S= N

The US got in (of course), added 60 aircrafts and the new ratio is 3:5

i.e. S+60 / N = 3/5

S+60/ 3S = 3/5

5S + 300 = 9S

S original= 75

S new = 75 +60 = 135

N = 3S = 3* 75= 225

All = S new + N = 135 + 225 = 360

[milanproda]

Dure, sorry for the late reply, but thanks!

I am curious, do you set up a proportion similar to the one you did in this problem for most ratio questions?