Set up two equations
Let n = one number
Let m = the second smaller number.
n + m = 30n+m=30
n - m = 6n−m=6
Solve the second equation for n
n - m + m = 6 +m n−m+m=6+m This gives
n = m + 6n=m+6 Now put ( m+6) in for n in the first equation.
m + 6 + m = 30m+6+m=30 using the communicative property gives
m + m + 6 = 30m+m+6=30 adding gives
2m + 6 = 30 2m+6=30 subtracting 6 from both sides gives
2m + 6 -6 = 30 -6 2m+6−6=30−6 which gives
2m = 24 2m=24 divide both sides by 2
(2m)/2 = 24/22m2=242 so
m = 12 m=12 the smaller number is 12 now substitute 12 into the second equation.
n - 12 = 6n−12=6 add 12 to both sides
n -12 + 12 = 6 + 12 n−12+12=6+12 this results in
n = 18 n=18 the larger number is 18
the two numbers are 18 and 12