i am a 3digit number that is less than 500. My ones digit is twice the hundreds digit. The sum of the three digits is 14. What number am I?
a b c
c = 2 a
a + b + c = 14
a b 2a
3 a + b = 14
ones digit is even
1 b 2 ---> 3+b=14, b = 11 no
2 b 4 ----> 6 + b =14, b = 8 ok
so
2 8 4
Let's break down the information given:
1. The number is a three-digit number.
2. The number is less than 500.
3. The ones digit is twice the hundreds digit.
4. The sum of the three digits is 14.
Let's solve this step-by-step based on the information given.
Step 1: The sum of the three digits is 14.
Let's consider the sum of the three digits of the number and determine the possible combinations that add up to 14:
0 + 5 + 9 = 14
1 + 4 + 9 = 14
2 + 3 + 9 = 14
2 + 4 + 8 = 14
3 + 4 + 7 = 14
4 + 5 + 5 = 14
Step 2: The ones digit is twice the hundreds digit.
From the possible combinations obtained in step 1, we need to consider the ones digit being twice the hundreds digit. Let's calculate the possible values of the hundreds and ones digits for each combination:
0 + 5 + 9 = hundreds digit: 0, ones digit: 9 (not valid)
1 + 4 + 9 = hundreds digit: 1, ones digit: 9 (not valid)
2 + 3 + 9 = hundreds digit: 2, ones digit: 9 (not valid)
2 + 4 + 8 = hundreds digit: 2, ones digit: 8 (valid)
3 + 4 + 7 = hundreds digit: 3, ones digit: 7 (not valid)
4 + 5 + 5 = hundreds digit: 4, ones digit: 5 (valid)
Step 3: The number is less than 500.
We need to choose the valid combinations from step 2 that are less than 500:
2 + 4 + 8 = 248 (valid)
4 + 5 + 5 = 455 (valid)
Based on the given conditions, the possible numbers are 248 and 455.
To find the answer to this problem, we need to break it down into smaller steps.
Step 1: Establish the conditions.
You are a three-digit number that is less than 500. Your ones digit is twice the hundreds digit, and the sum of the three digits is 14.
Step 2: Let's consider the hundreds digit.
We know that the ones digit is twice the hundreds digit. Since the ones digit cannot be greater than 9, the hundreds digit must be no greater than 4 (half of the maximum ones digit).
Step 3: Find possible values for the hundreds digit.
Given that the hundreds digit is no greater than 4, we can try all the possible values: 0, 1, 2, 3, 4.
Step 4: Find possible values for the ones digit.
The ones digit is twice the hundreds digit. So for each possible value of the hundreds digit, we can multiply it by 2 to find the corresponding value for the ones digit.
For example:
If the hundreds digit is 0, the ones digit is 0 x 2 = 0.
If the hundreds digit is 1, the ones digit is 1 x 2 = 2.
If the hundreds digit is 2, the ones digit is 2 x 2 = 4.
If the hundreds digit is 3, the ones digit is 3 x 2 = 6.
If the hundreds digit is 4, the ones digit is 4 x 2 = 8.
Step 5: Find the remaining tens digit.
We know that the sum of the three digits is 14, so we can subtract the hundreds digit and the ones digit from 14 to find the value of the tens digit.
For example:
If the hundreds digit is 0 and the ones digit is 0, then the sum of the tens digit and the other two digits must equal 14. Thus, the tens digit is 14 - 0 - 0 = 14.
If the hundreds digit is 1 and the ones digit is 2, then the tens digit is 14 - 1 - 2 = 11.
If the hundreds digit is 2 and the ones digit is 4, then the tens digit is 14 - 2 - 4 = 8.
If the hundreds digit is 3 and the ones digit is 6, then the tens digit is 14 - 3 - 6 = 5.
If the hundreds digit is 4 and the ones digit is 8, then the tens digit is 14 - 4 - 8 = 2.
Step 6: Check the possibilities.
Now that we have determined possible values for the hundreds, tens, and ones digits, we can construct the three-digit numbers using these values.
For example:
If the hundreds, tens, and ones digits are 0, 0, and 0 respectively, then the number is 000. However, since the number has to be less than 500, this is not a valid solution.
If the hundreds, tens, and ones digits are 1, 1, and 2 respectively, then the number is 112, which satisfies all the given conditions.
If the hundreds, tens, and ones digits are 2, 8, and 4 respectively, then the number is 284, which also satisfies the given conditions.
If the hundreds, tens, and ones digits are 3, 5, and 6 respectively, then the number is 356, which is less than 500 and satisfies all the given conditions.
If the hundreds, tens, and ones digits are 4, 2, and 8 respectively, then the number is 428, which also satisfies the given conditions.
Step 7: Determine the correct answer.
From the possible answers we found in step 6 (112, 284, 356, 428), the correct answer is the smallest one that satisfies all the given conditions. Therefore, the number you are is 112.