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 = 1,680
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 = 1,657
Therefore, the two Numbers are 1,680 and 1,657
Check Sum of the two Numbers:
1,680 + 1,657 = 3,337 ✓
Check Difference between the two Numbers:
1,680 − 1,657 = 23 ✓
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 =
3,337 + 23/2
x =
3,360/2
x = 1,680
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 =
3,337 − 23/2
y =
3,314/2
y = 1,657
Therefore, the two Numbers are 1,680 and 1,657
Check Sum of the two Numbers:
| 1 | 1 | |||
| 1 | 6 | 8 | 0 | |
| 1 | 6 | 5 | 7 | |
| 3 | 3 | 3 | 7 |
Check Difference between the two Numbers:
| 7 | 10 | |||
| 1 | 6 | 8 | 0 | |
| − | 1 | 6 | 5 | 7 |
| 2 | 3 |
