There is a certain number less than 100. The sum of the digits is 7 and the product of the digits is 6. What is the number?

we describe the number as 100=xy so that x is in the 10's place and y in the 1's place, then: 
1) x+y=7
2) xy=6 

x=6/y 
6/y+y=7
6+y^2=7y
y^2-7y+6=0
(y-6)(y-1)=0 
y=6 or y=1 

so we see that there are two numbers possible: 16 and 61