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 = 105.5
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 = 104.5
Therefore, the two Numbers are 105.5 and 104.5
Check Sum of the two Numbers:
105.5 + 104.5 = 210 (trailing zero and decimal point are dropped) ✓
Check Difference between the two Numbers:
105.5 − 104.5 = 1 (trailing zero and decimal point are dropped) ✓
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 =
210 + 1/2
x =
211/2
x = 105.5
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 =
210 − 1/2
y =
209/2
y = 104.5
Therefore, the two Numbers are 105.5 and 104.5
Check Sum of the two Numbers:
| 1 | 1 | ||||
| 1 | 0 | 5 | . | 5 | |
| 1 | 0 | 4 | . | 5 | |
| 2 | 1 | 0 | . | 0 |
Check Difference between the two Numbers:
| 1 | 0 | 5 | . | 5 | |
| − | 1 | 0 | 4 | . | 5 |
| 1 | . | 0 |
