The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit, and the tens digit equals to the sum of the other two. Find the number.
h + t + u = 6
h = 2 u
t = h + u ... 2 t = 6 ... t = 3
h + u = 3 ... 3 u = 3 ... u = 1
h + 3 + 1 = 6 ... h = 2
To find the three-digit number, we can start by setting up the equations based on the given information.
Let's assume the three-digit number is represented as ABC, where A is the hundreds digit, B is the tens digit, and C is the units digit.
We are given the following information:
1) The sum of the digits is 6: A + B + C = 6
2) The hundreds digit is twice the units digit: A = 2C
3) The tens digit equals the sum of the other two: B = A + C
Now we can solve these equations step by step to find the values of A, B, and C.
From equation 2, we have A = 2C. We can substitute this value in equation 3:
B = A + C
B = 2C + C
B = 3C
Now, we can substitute the value of B in equation 1:
A + B + C = 6
2C + 3C + C = 6
6C = 6
C = 1
Since C = 1, we can substitute this value back into A and B to find their respective values:
A = 2C = 2(1) = 2
B = 3C = 3(1) = 3
So, the three-digit number is 213.