We are given the following information about the magnets in the bag:
- There are 36 small magnets.
- The number of large magnets is half the number of small magnets.
- There are 8 large red magnets.
- The total number of white magnets is 5 times the total number of red magnets.
We need to determine how many small white magnets are in the bag. Let's proceed step by step.
1. Calculate the number of large magnets:
Given that the number of large magnets is half the number of small magnets:
[tex]\[
\text{Number of large magnets} = \frac{36}{2} = 18
\][/tex]
2. Calculate the total number of magnets:
[tex]\[
\text{Total number of magnets} = \text{Number of small magnets} + \text{Number of large magnets} = 36 + 18 = 54
\][/tex]
3. Calculate the total number of red magnets:
Given that there are 8 large red magnets and the rest are small red magnets, let’s denote the total number of red magnets by [tex]\( R \)[/tex]. According to the problem statement, large red magnets are 8 and the total red magnets include small red plus these large red:
[tex]\[
R = 36 - \left(\frac{18}{2}\right) = 36 - 9 = 27
\][/tex]
4. Calculate the total number of white magnets:
Given that there are 5 times as many white magnets as red magnets:
[tex]\[
\text{Total number of white magnets} = 5 \times \text{Number of red magnets} = 5 \times 27 = 135
\][/tex]
5. Calculate the number of large white magnets:
The total number of large magnets is 18 and there are 8 large red magnets, so:
[tex]\[
\text{Number of large white magnets} = 18 - 8 = 10
\][/tex]
6. Calculate the number of small white magnets:
Knowing the total number of white magnets and the number of large white magnets, we can find the number of small white magnets:
[tex]\[
\text{Number of small white magnets} = \text{Total number of white magnets} - \text{Number of large white magnets} = 135 - 10 = 125
\][/tex]
Therefore, the number of small white magnets in the bag is:
[tex]\[
\boxed{125}
\][/tex]
