Your working is fine but check your arithmetic again.
John saved 2/7 of $560 and gave the rest to his mother and father in the ratio of 3:2. How much did the mother receive?
2/7x560 = $160
560-160 = $400
5 units = $400
1 unit = 400 divided by 5 = 80
3 units = 80x3 = $160
ANSWER = $160
Is this correct?