The sum of the digits in a three digit number is nine.The tens digit is half the sum of the other two and the hundreds digit is half the unit digit.Find the total value of the second digit

h + t + u = 9

2 t = h + u

solve for t

a+b+c=9

2b=a+c

and u = 2h

What is the answer?

t=h+u/2

Well, let's break this down one digit at a time. We know that the sum of the digits is nine, so that means the three digits must add up to nine. Since the hundreds digit is half the unit digit, and the tens digit is half the sum of the other two digits, we can set up some equations.

Let's call the hundreds digit "h", the tens digit "t", and the unit digit "u".

Our first equation is h + t + u = 9, since the sum of the digits is nine.

Our second equation is t = (h + u)/2, since the tens digit is half the sum of the other two digits.

Our third equation is h = u/2, since the hundreds digit is half the unit digit.

Now, let's solve these equations simultaneously.

From the third equation, we can substitute h = u/2 into the first equation:
(u/2) + t + u = 9
(3/2)u + t = 9

Next, let's substitute t = (h + u)/2 into the first equation:
h + ((h + u)/2) + u = 9
3h + 2u = 18
Similarly, we can substitute h = u/2 into this equation:
3(u/2) + 2u = 18
(3/2)u + 2u = 18
(7/2)u = 18
u = (2/7) * 18
u = 36/7

Now that we know the value of the unit digit (approximately 5.142857), we can find the value of the tens digit by substituting u into the second equation:
t = (h + u)/2
t = (u/2) + u
t = (1/2)u + u
t = (3/2)u
t = (3/2)(36/7)
t = 54/7

Therefore, the value of the second digit (tens digit) is approximately 7.7142857.

To find the value of the second digit, we need to solve the given conditions step by step.

Let's assume the three-digit number as ABC, where A is the hundreds digit, B is the tens digit, and C is the units digit.

Given conditions:
1. The sum of the digits in a three-digit number is nine: A + B + C = 9
2. The tens digit is half the sum of the other two: B = (A + C)/2
3. The hundreds digit is half the unit digit: A = C/2

To solve these conditions, we will substitute the third condition into the second condition and solve for B.

Substituting A = C/2 into B = (A + C)/2, we get:
B = ((C/2) + C)/2
B = (3C/2)/2
B = 3C/4

Now, substitute B and A into the first condition and solve for C.

A + B + C = 9
(C/2) + (3C/4) + C = 9
(4C + 6C + 8C)/8 = 9
18C = 72
C = 4

Now, substitute the found value of C back into the third condition to find A.

A = C/2
A = 4/2
A = 2

Finally, substitute the values of A = 2 and C = 4 into the second condition to find B.

B = (A + C)/2
B = (2 + 4)/2
B = 6/2
B = 3

Therefore, the value of the second digit (tens digit) is 3.

The total value of the second digit is 3.