Any 3 digit number can be expressed in the form of:
[tex](a*100)+(b*10)+(c*1)[/tex]
Where [tex]a, b, c[/tex] represent any natural number from 0 to 9.
We are told the hundreds number (this means [tex]a*100[/tex] in the expression above) is equal to the value of 40 tens, 40 tens is 400. Then, we know the digit in the tens is greater then 6, this means [tex]b>6[/tex] in the expression above.
So, there are multiple numbers the room number could be, namely:
[tex]400+(b*10)+(c*1)\\[/tex]
where [tex]b[/tex] can be 7, 8, or 9; and [tex]c[/tex] can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So, there's 30 possible room numbers Lydia may be.
