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 = 113
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 = 25
Therefore, the two Numbers are 113 and 25
Check Sum of the two Numbers:
113 + 25 = 138 ✓
Check Difference between the two Numbers:
113 − 25 = 88 ✓
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 =
138 + 88/2
x =
226/2
x = 113
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 =
138 − 88/2
y =
50/2
y = 25
Therefore, the two Numbers are 113 and 25
Check Sum of the two Numbers:
| 1 | 1 | 3 | |
| 2 | 5 | ||
| 1 | 3 | 8 |
Check Difference between the two Numbers:
| 10 | |||
| 0 | 0 | 13 | |
| 1 | 1 | 3 | |
| − | 2 | 5 | |
| 8 | 8 |
