To determine the total length of twine that was originally on the spool, we need to sum the amount of twine given to the neighbor with the amount of twine that is left on the spool.
1. First, convert the mixed numbers to improper fractions or decimal form to make addition easier.
The amount of twine given to the neighbor:
[tex]\( 13 \frac{2}{3} \)[/tex] feet. This can be converted to a decimal as follows:
[tex]\[
13 \frac{2}{3} = 13 + \frac{2}{3} \approx 13 + 0.6666666666666666 = 13.666666666666666
\][/tex]
The amount of twine left on the spool:
[tex]\( 38 \frac{2}{5} \)[/tex] feet. This can be converted to a decimal as follows:
[tex]\[
38 \frac{2}{5} = 38 + \frac{2}{5} \approx 38 + 0.4 = 38.4
\][/tex]
2. Now, add these two decimal values to get the total amount of twine that was originally on the spool:
[tex]\[
13.666666666666666 + 38.4 = 52.06666666666666
\][/tex]
So, the total length of twine that was originally on the spool is approximately [tex]\( 52.06666666666666 \)[/tex] feet.
