Question

Ab + cd = aaa, where ab and cd are two-digit numbers and aaa is a three digit number; a, b, c, and d are distinct positive integers. In the addition problem above, what is the value of c?

Answer 1

Answer:

9

Step-by-step explanation:

Each a, b, c, d is a natural number.

0 < a ≤ 1

∴ a = 1

10 + b + 10c + d = 111

10c + b + d = 101

b, c, d are less than 10 and greater than 0

If c < 9, there are no b and d that satisfies the equation. (10c + b + d = 101)

9 ≤ c < 10

∴ c = 9