Both my hundreds and units digits are one-half of my tens digit. The sum of my three digits is 16. What am I.
let the tend digit be 2x
then the unit digit and the hundreds digit are each x
x+2x+x = 16
4x=16
x = 4
you are 484
To solve this problem, let's come up with a plan:
1. Define variables: Let's use the variables T, H, and U to represent the tens, hundreds, and units digits, respectively.
2. Translate the given information into equations:
- "Both my hundreds and units digits are one-half of my tens digit." gives us the equations H = (1/2)T and U = (1/2)T.
- "The sum of my three digits is 16." gives us the equation T + H + U = 16.
3. Simplify the equations:
- Since H = (1/2)T, we can substitute this expression into the equation T + H + U = 16, which gives us T + (1/2)T + (1/2)T = 16.
4. Solve the equation:
- Combining like terms, we get (2/2)T + (1/2)T + (1/2)T = 16.
- Simplifying further, we have (4/2)T = 16, or 2T = 16.
- Dividing both sides by 2, we find that T = 8.
5. Find the values of H and U:
- Since H = (1/2)T and U = (1/2)T, we substitute T = 8 into these equations, giving us H = 4 and U = 4.
6. Determine the final number:
- The final number consists of the digits T, H, and U in that order. So, the number is 8,444.
Therefore, the number you are is 8,444.