The sum of two natural numbers is 212.What are the numbers if the larger number divided by the smaller number gives the quotient 3 and the reminder...

Let x and y be the natural
numbers.

The sum of these natural numbers is
212.

x + y = 212 (1)

Let x be
larger than y.

We'll write the reminder theorem to express
the 2nd constraint.

x = 3y + 4
(2)

We'll replace (2) in
(1):

3y + 4 + y = 212

We'll
combine like terms and we'll subtract 4 both sides:

4y =
212 - 4

4y = 208 => y =
52

x = 3*52 + 4

x =
160

The required two natural numbers, that
respect the given constraints, are: x = 160 and y =
52.