Answer:

Omar's original number ---- x

Ray's original number ---- y

(1/5)x = (1/3)y

y = (3/5)x

After the gifting:

Ray has y-24

Omar will have x + 24

x+24 = 3(y-24

x - 3y = -96

sub in first part:

x - 3(3/5)x = -96

times 5

5x - 9x = -480

x = 120

then y = (3/5)(120) = 72

Omar had 120 and Ray had 72

check: (1/5)(120) = 24

(1/3)(72) = 24, well that checks out

after gift:

ray has 72 - 24 = 48

Omar will have 120+24 = 144

is 144 equal to 3 times 48