let 'x' and 'y' represent the numbers and let 'x' be the smaller (x < y)

The difference between two numbers is 3:

y - x = 3

If four times the smaller is divided by the larger, the quotient is 5:

4x/y = 5 multiply both sides by y

4x = 5y

by solving the system of equations:

y - x = 3

4x = 5y

we find:

x = -15

y = -12

click here to see the step by step solution of the system of equations:

the two numbers are -15 and -12.