Eleven members of the middle school math club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. they paid their guest speaker $1−a−2−. what is the missing digit a of this 3-digit number?

So, it's a 3 digit number that is divisible by 11, and starts with a 1, and ends with a 1.

each of them paid the same amount, let's say y and we know that if we multiply this y by 11, we'll have a number with a "2" at the end: so the last digit of y must be 2, since only 2*1=2

also, the first digit of y must be 1, since the first digit of the 3-digit number is 1.

so lets try what happens if they all pay 12 dollars? the sum is 132, so A must be 3!!!