Question

The sum of two numbers, a and b, is 12. Their difference is 8. Find the larger number.

Answer 1

Mathematically, assuming a is the larger number:
\[a+b=12\]
\[a-b=8\]

Answer 2

a + b = 12---> a = 12 - b
a - b = 8

a - b = 8
12 - b - b = 8
12 - 2b = 8
12 - 8 = 2b
4 = 2b
2 = b

a + b = 12
a + 2 = 12
a = 12 - 2
a = 10

check...
a + b = 12
10 + 2 = 12
12 = 12 (correct)

or ...
a - b = 8
10 - 2 = 8
8 = 8 (correct)

ANSWER : Larger number is 10. Smaller number is 2