# 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 4 ?

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Let the numbers be A and B, where A is the larger number

Their sum is 212

=> A + B = 212

The larger number divided by the smaller number gives a quotient 3 and a reminder 4

=> A = 3B + 4

Substitute in A + B = 212

=> 3B + 4 + B = 212

=> 4B + 4 = 212

=> 4B = 208

=> B = 52

A = 212 - 52 = 160

**The numbers are 160 and 52.**

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.**