The sum of two numbers is 9.9, and the sum of the squares of the numbers is 53.21. What are the numbers?

There are two possibilities:

and

and

Step-by-step explanation:

Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:

First, is cleared in the first equation:

Now, the variable is substituted in the second one:

And some algebra is done in order to simplify the expression:

Roots are found by means of the General Equation for Second-Order Polynomials:

and

There are two different values for :

There are two possibilities:

and

and

answer: 12/52

step-by-step explanation: my reasoning is that there are 12 face cards in a deck and a total of 52 cards in all.