The difference of two numbers is 30. their quotient is 6. what are the two numbers

Well, the quotient must be bigger/smaller

lets say the numbers are x and y

x>y

so

x-y=30 and x/y=6

multiply both sides by y in 2nd equation

x=6y

subsitute 6y for x in other equation

6y-y=30

5y=30

divide by 5

y=6

sub back

x=6y

x=6 (6)

x=36

the numbers are 36 and 6

but they could also be - 36 and - 6 because - 36/-6=6 and - 6 - (-36) = 30

the 2 numbers are 36 and 6 or - 36 and - 6