Final answer:
To find the 3-digit number, let the hundreds digit be a, the tens digit be b, and the units digit be c. The sum of all three digits is a + b + c, which is equal to the sum of the digits at the tens and hundreds place, a + b. By subtracting a + b from both sides of the equation, we find that the units digit, c, is 0. Since the hundreds digit cannot be 0, the only possibility is that it is 1. Therefore, the number is 1ab, where a is the hundreds digit and b is the tens digit.
Step-by-step explanation:
To find the 3-digit number that satisfies the given condition, we can use algebraic representation. Let the hundreds digit be a, the tens digit be b, and the units digit be c. The sum of all three digits is a + b + c. According to the condition, this sum is equal to the sum of the digits at the tens and hundreds place, which is a + b. Therefore, we have the equation a + b + c = a + b. Subtracting a + b from both sides of the equation, we get c = 0. So the units digit is 0. Since the number is a 3-digit number, the hundreds digit cannot be 0. Therefore, the only possibility is that the hundreds digit is 1. Hence, the number is 1ab, where a is the hundreds digit and b is the tens digit.