Two numbers are in the ratio of  6 : 5. If their sum is 22, then what is the sum of the squares of the two numbers?

The ratio of two numbers is 6 : 5.

Their sum is 22.

If two numbers are in the ratio a : b, their actual values can be expressed as:

First number = ax, Second number = bx,

where x is a common multiplier.

The sum of their squares is:

​$$\text{Sum of squares} = (\text{First number})^2 + (\text{Second number})^2$$ 

Solution: 

Let the number be 6x and 5x.

According to the question;

6x + 5x = 22 

11x = 22 

x = 2 

So, the number is $$6x = 6 \times 2 = 12 , \ \ \ \ \text{ and} \ \ \ \ \ \ 5x = 5 \times2 = 10$$ 

Sum of square of the numbers are 

​$$= (12)^2 + (10)^2 = 144 + 100 = 244$$​​