One number exceeds another by 12 . if five times the smaller number is subtracted from three times the larger number the result is 20. Find the numbers

y = x+12

3y-5x = 20

14 x = -40

y = -28

To solve this problem, we'll use algebraic equations. Let's assume the smaller number is represented by "x" and the larger number is represented by "y".

According to the problem:
1) One number exceeds another by 12.
This can be written as: y = x + 12

2) Five times the smaller number is subtracted from three times the larger number, and the result is 20.
This can be written as: 3y - 5x = 20

Now, we have a system of two equations:
y = x + 12
3y - 5x = 20

There are different methods to solve this system, such as substitution or elimination. Let's use substitution.

Step 1: Solve the first equation for y.
y = x + 12

Step 2: Substitute the value of y in the second equation.
3(x + 12) - 5x = 20

Step 3: Solve for x.
3x + 36 - 5x = 20
-2x + 36 = 20
-2x = 20 - 36
-2x = -16
x = -16 / -2
x = 8

Step 4: Substitute the value of x into either of the original equations to find y.
y = x + 12
y = 8 + 12
y = 20

So, the smaller number (x) is 8 and the larger number (y) is 20.