Why can't 4 two - digit addends be greater then 400?

Answer 1

404

Answer 2

Each one of them is smaller than 100.

So 4 of them will be less than 4 lots of 100 or 400.

To prove that statement:

Suppose the 4 numbers are a, b, c and d.

Each of them is less than 100.

a < 100 so a = 100 - w for some positive number w.

Similarly, b = 100 - x; c = 100 - y; and d = 100 - z where x, y and z are also positive numbers.

Adding these 4 together,

a + b + c + d = 100 - w + 100 - x + 100 - y + 100 - z

= 400 - (w + x + y + z)

Now each of w, x, y and z is positive. Therefore, w+x+y+z is positive (the set of positive numbers is closed under addition).

So a + b + c + d = 400 - some positive number

ie a + b + c + d < 400