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 = 115.6
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 = 84.4
Therefore, the two Numbers are 115.6 and 84.4
Check Sum of the two Numbers:
115.6 + 84.4 = 200 (trailing zero and decimal point are dropped) ✓
Check Difference between the two Numbers:
115.6 − 84.4 = 31.2 ✓
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 + 31.2/2
x =
231.2/2
x = 115.6
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 − 31.2/2
y =
168.8/2
y = 84.4
Therefore, the two Numbers are 115.6 and 84.4
Check Sum of the two Numbers:
1 | 1 | 1 | |||
1 | 1 | 5 | . | 6 | |
+ | 8 | 4 | . | 4 | |
2 | 0 | 0 | . | 0 |
Check Difference between the two Numbers:
0 | 11 | ||||
1 | 1 | 5 | . | 6 | |
− | 8 | 4 | . | 4 | |
3 | 1 | . | 2 |