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 = 118.5
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 = 81.5
Therefore, the two Numbers are 118.5 and 81.5
Check Sum of the two Numbers:
118.5 + 81.5 = 200 (trailing zero and decimal point are dropped) ✓
Check Difference between the two Numbers:
118.5 − 81.5 = 37 (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 =
200 + 37/2
x =
237/2
x = 118.5
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 =
200 − 37/2
y =
163/2
y = 81.5
Therefore, the two Numbers are 118.5 and 81.5
Check Sum of the two Numbers:
| 1 | 1 | 1 | |||
| 1 | 1 | 8 | . | 5 | |
| 8 | 1 | . | 5 | ||
| 2 | 0 | 0 | . | 0 |
Check Difference between the two Numbers:
| 0 | 11 | ||||
| 1 | 1 | 8 | . | 5 | |
| − | 8 | 1 | . | 5 | |
| 3 | 7 | . | 0 |
