Let the number of lengths Stephenie swims on the first day be denoted as \( x \).
On the second day, she swims \( x + 5 \) lengths, and on the third day, she swims \( x + 10 \) lengths.
We can set up the following equation to represent the total lengths she swims over the 3 days:
\[ x + (x + 5) + (x + 10) = 108 \]
Combining like terms gives:
\[ 3x + 15 = 108 \]
To isolate \( 3x \), we subtract 15 from both sides:
\[ 3x = 108 - 15 \] \[ 3x = 93 \]
Next, we divide by 3 to solve for \( x \):
\[ x = \frac{93}{3} = 31 \]
Now that we have \( x \), we can determine the number of lengths she swims on each day:
- First day: \( x = 31 \)
- Second day: \( x + 5 = 31 + 5 = 36 \)
- Third day: \( x + 10 = 31 + 10 = 41 \)
Thus, the number of lengths Stephenie swims on the last day is:
\[ \boxed{41} \]
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