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 = 87
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 = 32
Therefore, the two Numbers are 87 and 32
Check Sum of the two Numbers:
87 + 32 = 119 ✓
Check Difference between the two Numbers:
87 − 32 = 55 ✓
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 =
119 + 55/2
x =
174/2
x = 87
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 =
119 − 55/2
y =
64/2
y = 32
Therefore, the two Numbers are 87 and 32
Check Sum of the two Numbers:
| 1 | |||
| 8 | 7 | ||
| 3 | 2 | ||
| 1 | 1 | 9 |
Check Difference between the two Numbers:
| 8 | 7 | |
| − | 3 | 2 |
| 5 | 5 |
