The sum of digits in a three digit number is nine. The tens digit is half the other two and the hundreds digit is half the units digits. Find the total value of the number
If the digits are xyz, then
x+y+z=9
2y=x+z
2x=z
The number is thus 234
To solve this problem, let's break it down step by step.
Step 1: Define the variables.
Let's represent the hundreds digit as "H," the tens digit as "T," and the units digit as "U."
Step 2: Translate the given information into equations.
From the problem statement, we have two conditions:
1) The sum of the digits is nine: H + T + U = 9
2) The tens digit is half the sum of the other two digits: T = (1/2)(H + U)
3) The hundreds digit is half the units digit: H = (1/2)U
Step 3: Simplify the equations.
We can simplify equation 3) by multiplying both sides by 2 to remove the fraction: 2H = U.
Now we can substitute this value of U into equations 1) and 2) to express them in terms of H only.
In equation 2), we can substitute (1/2)U with (1/2)(2H), which simplifies to T = H.
In equation 1), we can substitute U with 2H, which gives us: H + T + 2H = 9; combining like terms: 3H + T = 9.
Step 4: Solve the equations.
We now have two equations:
1) T = H
2) 3H + T = 9
We can use trial and error to find the values of H and T that satisfy both equations, but to simplify the process, let's look for whole number solutions within a reasonable range.
Given that the digits are between 0 and 9, let's try H = 1, 2, 3, and so on, until we reach a solution.
When H = 1, we have T = 1 from equation 1) and 3H + T = 3 + 1 = 4, not equal to 9.
When H = 2, we have T = 2 from equation 1) and 3H + T = 6 + 2 = 8, not equal to 9.
When H = 3, we have T = 3 from equation 1) and 3H + T = 9 + 3 = 12, not equal to 9.
However, when H = 4, we have T = 4 from equation 1) and 3H + T = 12 + 4 = 16, not equal to 9.
Finally, when H = 5, we have T = 5 from equation 1) and 3H + T = 15 + 5 = 20, not equal to 9.
Since no whole number solutions satisfy both equations, it seems that the problem may have been mistyped or described incorrectly. Please double-check the given information.