The sum of a 3 digit number and a 1 digit number is 217. the product of the numbers is 642. if one number is between 200 and 225, what are the numbers?

Let, the numbers be "x" and "y". Consider "x" as the triple digit number.
Now, according to the question,
x + y = 217..........................equation (1)

x * y = 642............................equation (2)

Now,
Taking equation (2),
x * y = 642
y = 642 / x..................................equation (3)

Now, Taking equation (1),


Substituting the value of y from equation (3), we get,



















Using zero product property,
EITHER,
           x - 3 = 0
                x = 3
OR,
          x - 214 = 0
                  x  = 214
Since, "x" is the triple digit number, x = 214.
Now,
Taking equation (2),
x * y = 642
Substituting the value of "x" in the equation, we get,
(214) * y = 642
y = 642 / 214
y = 3

So, the numbers are 214 and 3.