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 =
Find x by substituting given Sum and Difference into equation for x and simplify:
x =
x =
x = 88
Solve the system of equations for y (smaller number):
y =
Find y by substituting given Sum and Difference into equation for y and simplify:
y =
y =
y = 52
Therefore, the two Numbers are 88 and 52
Check Sum of the two Numbers:
88 + 52 = 140 ✓
Check Difference between the two Numbers:
88 − 52 = 36 ✓
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 =
140 + 36/2
x =
176/2
x = 88
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 =
140 − 36/2
y =
104/2
y = 52
Therefore, the two Numbers are 88 and 52
Check Sum of the two Numbers:
| 1 | 1 | ||
| 8 | 8 | ||
| 5 | 2 | ||
| 1 | 4 | 0 |
Check Difference between the two Numbers:
| 8 | 8 | |
| − | 5 | 2 |
| 3 | 6 |
