Let's go through the steps to solve this problem:
1. Identify the given quantities:
- Number of brooms: 8
- Number of mops: 6
2. Calculate the total number of items:
- Total number of brooms and mops = [tex]\( 8 + 6 = 14 \)[/tex]
3. Calculate the ratio:
- The ratio of the number of mops to the total number of items is calculated by dividing the number of mops by the total number of items.
[tex]\[
\text{Ratio} = \frac{\text{Number of mops}}{\text{Total number of items}} = \frac{6}{14}
\][/tex]
4. Simplify the ratio:
- The fraction [tex]\(\frac{6}{14}\)[/tex] can be simplified by finding the greatest common divisor (GCD) of 6 and 14, which is 2.
[tex]\[
\frac{6}{14} = \frac{6 \div 2}{14 \div 2} = \frac{3}{7}
\][/tex]
Therefore, the ratio of the number of mops to the total number of brooms and mops is [tex]\(\frac{3}{7}\)[/tex].
So, the correct answer is:
C. [tex]\(\frac{3}{7}\)[/tex]
