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 = 18.5
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 = 11.5
Therefore, the two Numbers are 18.5 and 11.5
Check Sum of the two Numbers:
18.5 + 11.5 = 30 (trailing zero and decimal point are dropped) ✓
Check Difference between the two Numbers:
18.5 − 11.5 = 7 (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 =
30 + 7/2
x =
37/2
x = 18.5
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 =
30 − 7/2
y =
23/2
y = 11.5
Therefore, the two Numbers are 18.5 and 11.5
Check Sum of the two Numbers:
| 1 | 1 | |||
| 1 | 8 | . | 5 | |
| 1 | 1 | . | 5 | |
| 3 | 0 | . | 0 |
Check Difference between the two Numbers:
| 1 | 8 | . | 5 | |
| − | 1 | 1 | . | 5 |
| 7 | . | 0 |
