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 = 3,256
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 = 2,725
Therefore, the two Numbers are 3,256 and 2,725
Check Sum of the two Numbers:
3,256 + 2,725 = 5,981 ✓
Check Difference between the two Numbers:
3,256 − 2,725 = 531 ✓
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 =
5,981 + 531/2
x =
6,512/2
x = 3,256
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 =
5,981 − 531/2
y =
5,450/2
y = 2,725
Therefore, the two Numbers are 3,256 and 2,725
Check Sum of the two Numbers:
1 | ||||
3 | 2 | 5 | 6 | |
2 | 7 | 2 | 5 | |
5 | 9 | 8 | 1 |
Check Difference between the two Numbers:
2 | 12 | |||
3 | 2 | 5 | 6 | |
− | 2 | 7 | 2 | 5 |
5 | 3 | 1 |