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Question 460851: a three-digit number satisfies the following conditions: the digits are consecutive whole numbers; the sum of the digits is greater than 10 and less than 20; and the tens digit is ann odd number. what is the number?
Found 2 solutions by J2R2R, poliphob3.14:
Answer by J2R2R(94)   (Show Source):
You can put this solution on YOUR website! You could solve this with guesswork or mathematically, so let us look at it both ways.
Guesswork:
Three numbers in succession
1, 2, 3: too low since 1 + 2 + 3 = 6;
2, 3, 4: too low since 2 + 3 + 4 = 9;
3, 4, 5: okay since 3 + 4 + 5 = 12
4, 5, 6: okay since 4 + 5 + 6 = 15
5, 6, 7: okay since 5 + 6 + 7 = 18
6, 7, 8: too high since 6 + 7 + 8 = 21
We can see that we have three to choose form but the ten’s must be odd, so the only solution is 456.
Mathematically:
Let the three numbers be a - 1, a, a + 1 where a is the ten digit
The sum of the three digits is 3a which has to be between 10 and 20, so 3a = 12, 15 or 18 giving a = 4, 5 or 6.
The only odd value for a is 5, so the three digit number we have is 456.
Answer by poliphob3.14(115)  (Show Source):
You can put this solution on YOUR website! Let the tens digit = 2k+1, an odd number, then the hundreds digit is 2k and the units digit 2k+2, where k is a natural number. These digits must satisfy the conditions: 10 < 2k+2k+1+2k+2 <20 Solving these inequalities we get:
10< 6k+3 <20 => 7< 6k <20 => 7/6< k <20/7 These inequalities are equivalent to the inequalities: 1< k <3, since k is a natural number we conclude that k=1, and the digits of our number are: 2k=4; 2k+1=5 and 2k+2=6.
Answer: The number is 456, which satisfy our conditions.
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