Use each clue to find a three digit number
Sure! Please provide me with the clues, and I'll guide you on how to find the three-digit number step by step.
Clue 1: The hundreds digit is twice the tens digit.
To find the three-digit number, we need to determine the values of the hundreds, tens, and units digits. Let's represent the hundreds digit as H, the tens digit as T, and the units digit as U.
According to the clue, the hundreds digit (H) is twice the tens digit (T). So, we can write the equation: H = 2T.
Clue 2: The units digit is odd.
This clue tells us that the units digit (U) is an odd number. Therefore, it can be any of the digits 1, 3, 5, 7, or 9.
Clue 3: The sum of all three digits is 11.
The sum of the three digits (H + T + U) is 11. We can substitute H = 2T from clue 1 into this equation to simplify it: 2T + T + U = 11.
Now, let's go through all possible values for the units digit (U) and solve for the values of T and H based on the given clues:
1. If U = 1:
Substitute U = 1 into the equation: 2T + T + 1 = 11.
Simplify: 3T + 1 = 11.
Solve for T: 3T = 10, T = 10/3 (not a whole number).
2. If U = 3:
Substitute U = 3 into the equation: 2T + T + 3 = 11.
Simplify: 3T + 3 = 11.
Solve for T: 3T = 8, T = 8/3 (not a whole number).
3. If U = 5:
Substitute U = 5 into the equation: 2T + T + 5 = 11.
Simplify: 3T + 5 = 11.
Solve for T: 3T = 6, T = 2.
Therefore, H = 2T = 2(2) = 4.
The three-digit number is 425.
4. If U = 7:
Substitute U = 7 into the equation: 2T + T + 7 = 11.
Simplify: 3T + 7 = 11.
Solve for T: 3T = 4, T = 4/3 (not a whole number).
5. If U = 9:
Substitute U = 9 into the equation: 2T + T + 9 = 11.
Simplify: 3T + 9 = 11.
Solve for T: 3T = 2, T = 2/3 (not a whole number).
Therefore, the only three-digit number that satisfies all the given clues is 425.