To solve the problem of finding four different odd numbers that add up to 24, with none of them being greater than 13, and the two smallest odd numbers adding up to 6, follow these steps:
1. Identify the smallest odd numbers:
- We need two smallest odd numbers that add up to 6. The two smallest odd numbers are 1 and 5 because:
[tex]\[
1 + 5 = 6
\][/tex]
2. Calculate the remaining sum:
- Since the total sum of the four numbers should be 24, subtract the sum of the two smallest numbers from 24 to find the remaining sum:
[tex]\[
24 - 6 = 18
\][/tex]
- This means the sum of the remaining two odd numbers must be 18.
3. List the remaining possible odd numbers up to 13:
- The possible odd numbers up to 13 that can be used are 3, 7, 9, 11, and 13.
4. Determine the third and fourth numbers:
- To find two numbers from the list that sum to 18, we start by considering the smallest possible number:
- Third number: Let's consider 3. If 3 is used, the fourth number must be:
[tex]\[
18 - 3 = 15
\][/tex]
- However, 15 is greater than 13, and thus not allowed.
- Next, consider 7 as the third number. If 7 is used, the fourth number must be:
[tex]\[
18 - 7 = 11
\][/tex]
- Both 7 and 11 are valid odd numbers and fit the conditions provided (none is greater than 13).
5. Verify the numbers:
- We now have four odd numbers: 1, 5, 7, and 11.
- Check the sum:
[tex]\[
1 + 5 + 7 + 11 = 24
\][/tex]
Therefore, the four different odd numbers that sum up to 24, with none of them being greater than 13, and the two smallest adding up to 6, are:
[tex]\[
1, 5, 7, 11
\][/tex]
