Two Numbers with a Sum of 48 and a Difference of 12

Define variables:
Let x = larger number and y = smaller number
Resulting system of equations:
x + y = Sum
x − y = Difference
Solve the system of equations for x (larger number):
x =  

Sum + Difference/2

Find x by substituting given Sum and Difference into equation for x and simplify:
x =  
x =  
x =  30
Solve the system of equations for y (smaller number):
y =  

Sum − Difference/2

Find y by substituting given Sum and Difference into equation for y and simplify:
y =  
y =  
y =  18
Therefore, the two Numbers are 30 and 18
Check Sum of the two Numbers:

	3	0
	1	8
	4	8

30 + 18 = 48 ✓
Check Difference between the two Numbers:

	2	10
	3	0
−	1	8
	1	2

30 − 18 = 12 ✓