Question

Ray and Omar collect stamps. Originally, 1/5 of Omar’s stamps were equivalent to 1/3 of Ray’s stamps. If Ray gave Omar 24 stamps, Omar would have 3 times as many stamps as Ray.
Find the number of stamps each of them had in the beginning.

Answer 1

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

<b>Omar had 120 and Ray had 72</b>

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 ?? sure is!