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?