Hi Math Investigator,
Thanks for highlighting.
I rewrite the solution as below for reference.
After moving coins from Box A to Box B,
ratio of 50-cent to $1 in Box A becomes 1A : 1A
ratio of 50-cent to $1 in Box B becomes 3B : 7B
1A + 3B = 400 +160 = 560
1A + 7B = 180 +1100 = 1280
4B = 720
B = 180
3B = 180 * 3 = 540
value of 50-cent in Box B 540 * 0.50 = $270
Thanks again Priskhipo and Math Investigator.