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 = 181
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 = 97
Therefore, the two Numbers are 181 and 97
Check Sum of the two Numbers:
181 + 97 = 278 ✓
Check Difference between the two Numbers:
181 − 97 = 84 ✓
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 =
278 + 84/2
x =
362/2
x = 181
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 =
278 − 84/2
y =
194/2
y = 97
Therefore, the two Numbers are 181 and 97
Check Sum of the two Numbers:
| 1 | |||
| 1 | 8 | 1 | |
| 9 | 7 | ||
| 2 | 7 | 8 |
Check Difference between the two Numbers:
| 17 | |||
| 0 | 7 | 11 | |
| 1 | 8 | 1 | |
| − | 9 | 7 | |
| 8 | 4 |
