Question

The sum of the digits of a three-digit number is 12. The tens digit, t, is 2 more than the hundreds digit, h. The units digit, u, is equal to the sum of the tens and hundreds digits. What is the number?

The three-digit number is _____

Answer 1

By utilizing the given conditions and algebraic expression, it is determined that the three-digit number where the sum of its digits is 12, the tens digit is 2 more than the hundreds digit, and the units digit is the sum of the tens and hundreds of digits, is 246.

Step-by-step explanation:

The question asks us to find a three-digit number based on specific conditions related to its digits. To solve this, let's list out the given conditions and assign variables to each digit of the number:

• The sum of the digits is 12.
• The tens digit (t) is 2 more than the hundreds digit (h).
• The unit digit (u) is equal to the sum of the tens and hundreds digits (t + h).

Expressing the conditions algebraically, we get:

1. h + t + u = 12
2. t = h + 2
3. u = h + t

From the second condition, we can replace t in the other two equations:

1. h + (h + 2) + u = 12
2. u = h + (h + 2)

Combining the equations, we find:

2h + 2 + u = 12
u = 2h + 2

Then, we simplify and solve for h:

2h + 2 + (2h + 2) = 12
4h + 4 = 12
4h = 8
h = 2

Substituting h back into the conditions, we get:

1. t = 2 + 2 = 4
2. u = 2 + 4 = 6

Therefore, the three-digit number, based on the given conditions, is 246.