Answer:
30 and 18
Explanation:
The equations representing a "sum and difference" problem are easily solved using elimination or substitution.
Setup
Let 'a' and 'b' represent the two numbers.
a + b = 48 . . . . . the sum
a - b = 12 . . . . . . the difference
Solution
Add the two equations to eliminate 'b'.
2a = 60
a = 30 . . . . . . . divide by 2
b = 30 -12 = 18
The two numbers are 30 and 18.
__
Additional comment
You may have noticed that the larger of the two numbers is half the sum of the given numbers: a = (48+12)/2 = 30. Similarly, the smaller of the two numbers is half their difference: (48-12)/2 = 18.
This is the generic solution to a "sum and difference" problem, meaning you can often work it mentally and just write down the answer.