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 = 193
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 = 54
Therefore, the two Numbers are 193 and 54
Check Sum of the two Numbers:
193 + 54 = 247 ✓
Check Difference between the two Numbers:
193 − 54 = 139 ✓
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 =
247 + 139/2
x =
386/2
x = 193
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 =
247 − 139/2
y =
108/2
y = 54
Therefore, the two Numbers are 193 and 54
Check Sum of the two Numbers:
| 1 | |||
| 1 | 9 | 3 | |
| 5 | 4 | ||
| 2 | 4 | 7 |
Check Difference between the two Numbers:
| 8 | 13 | ||
| 1 | 9 | 3 | |
| − | 5 | 4 | |
| 1 | 3 | 9 |
