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 = 948
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 = 708
Therefore, the two Numbers are 948 and 708
Check Sum of the two Numbers:
948 + 708 = 1,656 ✓
Check Difference between the two Numbers:
948 − 708 = 240 ✓
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 =
1,656 + 240/2
x =
1,896/2
x = 948
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 =
1,656 − 240/2
y =
1,416/2
y = 708
Therefore, the two Numbers are 948 and 708
Check Sum of the two Numbers:
1 | 1 | |||
9 | 4 | 8 | ||
7 | 0 | 8 | ||
1 | 6 | 5 | 6 |
Check Difference between the two Numbers:
9 | 4 | 8 | |
− | 7 | 0 | 8 |
2 | 4 | 0 |