Final answer:
The two numbers are 4 and 16. The difference between two numbers is 12 and their quotient is 4. By solving the system of equations, we find that the larger number is 16 and the smaller number is 4.
Step-by-step explanation:
To find the two numbers, let's call them x and y. We know that the difference between the two numbers is 12, which can be written as:
x - y = 12
We also know that the quotient (or division) of the two numbers is 4, which can be written as:
x / y = 4
From the first equation, we can solve for x in terms of y by adding y to both sides:
x = y + 12
Now, substitute x = y + 12 into the second equation:
(y + 12) / y = 4
Multiply both sides by y to get rid of the fraction:
y + 12 = 4y
Subtract y from both sides:
12 = 4y - y
Combine like terms:
12 = 3y
Divide both sides by 3 to solve for y:
y = 4
Substitute y = 4 back into the equation x = y + 12:
x = 4 + 12
x = 16
Therefore, the two numbers are 4 and 16.