x has 3 digits. the tens digits is half the hundreds digits. the number is odd.the sum of the digits is 9
Let the tens digit be x. Then the hundreds digit is 2x. The sum of these two digits is 3x, and that has to be less than 9, so x must be less than 3 - that is, the tens digit must be 1 or 2.
So we might have:
42U or 21U
where U is the Units digit.
The digits add to 9, so it has to be
423 or 216
But we are told that the answer is odd, and only one of those is odd...
x + 2x = 3x
solve this first
where 3x < 9
3/3 x < 9/3 divide
both sides by 3
1x < or = 3 plug in 3 into the equation.
3 + 3*2 = 3*3
3 + 6 = 9
To find the number with the given conditions, let's go step by step:
Step 1: The number is odd.
Since the number is odd, the units digit must be 1, 3, 5, 7, or 9.
Step 2: The sum of the digits is 9.
Let's assume the hundreds digit is a. Then, we know that a + b + c = 9, where b is the tens digit and c is the units digit. Since the units digit is odd, it must be 1, 3, 5, 7, or 9. Let's substitute some values and see what works:
- If c = 1, then a + b + 1 = 9. We can see that no combination of a and b satisfies this condition.
- If c = 3, then a + b + 3 = 9. This means a + b = 6. The only possible values for a and b are 3 and 3.
- If c = 5, then a + b + 5 = 9. We can see that no combination of a and b satisfies this condition.
- If c = 7, then a + b + 7 = 9. We can see that no combination of a and b satisfies this condition.
- If c = 9, then a + b + 9 = 9. This means a + b = 0. We can see that no combination of a and b satisfies this condition.
Therefore, the only combination that satisfies the second condition is a = 3, b = 3, and c = 3.
Step 3: The tens digit is half the hundreds digit.
Since b = 3, and a = 3, we can see that the tens digit (b) is not half the hundreds digit (a). Therefore, there is no solution that satisfies all the given conditions.
In conclusion, there is no number that satisfies all the specified conditions.
To find the three-digit number that satisfies the given conditions, we can break down the problem step by step:
Step 1: Determine the hundreds digit.
Since the tens digit is half the hundreds digit, we can assign a variable to the unknown hundreds digit. Let's use the variable "h" for the hundreds digit. According to the given information, the tens digit is half the hundreds digit, so it would be h/2.
Step 2: Determine the tens digit.
Now that we have the hundreds digit (h) and know that the tens digit is half of it, we can express the tens digit using h/2.
Step 3: Determine the units digit.
The sum of the digits is 9, so we can set up the equation: h + h/2 + units digit = 9. Simplifying this equation, we have 2h + units digit = 9.
Step 4: Narrow down the possibilities.
Since the number is odd, the units digit must be an odd number. This means it can only be 1, 3, 5, 7, or 9.
Step 5: Check the possibilities.
Now, we can substitute each of the possible units digits into the equation 2h + units digit = 9 and solve for h.
For each of the possible units digits:
- If the equation does not have a whole number solution for h, discard that possibility.
- If the equation has a whole number solution for h, use that value to determine the tens digit and form the three-digit number.
By going through this process, you can find the specific hundreds, tens, and units digits that satisfy the given conditions and form the three-digit number.