Question 303960
The sum of the digits is 9. The product of the digits is 18. The number is between 40 and 90.
What is the number?
:
Let 10x + y = the two digit number
:
"The sum of the digits is 9."
x + y = 9
y = (9-x)
:
The product of the digits is 18.
x * y = 18
Replace y with (9-x)
x(9-x) = 18
-x^2 + 9x = 18
-x^2 + 9x - 18 = 0
Multiply by -1 to change the signs
x^2 - 9x + 18 = 0
Factors easily to
(x-6)(x-3) = 0
x = 6, (no. is greater than 40)
then 
y = 3
:
The number is between 40 and 90. 
What is the number? It's 63