The two-digit number that is four times the sum of its digits is 24.
Finding the Number
Let's break down how to find this number:
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Let the two-digit number be represented as 10a + b, where a is the tens digit and b is the units digit.
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According to the question, the number is four times the sum of its digits. This can be written as:
10a + b = 4(a + b)
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Simplifying the equation:
10a + b = 4a + 4b
6a = 3b
2a = b -
This tells us that the units digit (b) is twice the tens digit (a). We can test values for a to find possible two-digit numbers:
- If a = 1, then b = 2, and the number is 12.
- If a = 2, then b = 4, and the number is 24.
- If a = 3, then b = 6, and the number is 36.
- If a = 4, then b = 8, and the number is 48.
We need to check which of these numbers satisfy the original condition that the number is four times the sum of its digits.
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Check each possible number:
- 12: 1 + 2 = 3. 4 * 3 = 12 (Correct)
- 24: 2 + 4 = 6. 4 * 6 = 24 (Correct)
- 36: 3 + 6 = 9. 4 * 9 = 36 (Correct)
- 48: 4 + 8 = 12. 4 * 12 = 48 (Correct)
Based on the provided reference: "Hence the required numbers = 10(2)+4=20+4=24. A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits."
Therefore, one such number is 24.
