To solve this problem, we need to check which of the given options adds up to the total length of the scarf, which is \( \frac{15}{12} \) yards.
First, let's convert \( \frac{15}{12} \) to a simpler form: \[ \frac{15}{12} = \frac{5}{4} \text{ (or 1.25 yards)} \]
Now, adding up the fractions provided in each response we can check if they equal \( \frac{15}{12} \) or \( 1.25 \).
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Option 1: \( \frac{1}{12} + \frac{2}{12} + \frac{3}{12} + \frac{8}{12} + \frac{4}{12} \)
- Sum = \( \frac{1 + 2 + 3 + 8 + 4}{12} = \frac{18}{12} = \frac{3}{2} = 1.5 \)
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Option 2: \( \frac{1}{12} + \frac{6}{12} + \frac{3}{12} + \frac{2}{12} + \frac{4}{12} \)
- Sum = \( \frac{1 + 6 + 3 + 2 + 4}{12} = \frac{16}{12} = \frac{4}{3} \approx 1.33 \)
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Option 3: \( \frac{2}{12} + \frac{3}{12} + \frac{3}{12} + \frac{2}{12} + \frac{5}{12} \)
- Sum = \( \frac{2 + 3 + 3 + 2 + 5}{12} = \frac{15}{12} = 1.25 \)
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Option 4: \( \frac{5}{12} + \frac{1}{12} + \frac{4}{12} + \frac{2}{12} + \frac{5}{12} \)
- Sum = \( \frac{5 + 1 + 4 + 2 + 5}{12} = \frac{17}{12} \approx 1.42 \)
Now we can see that the only option that sums up to \( \frac{15}{12} \) (or \( 1.25 \) yards) is: Option 3: \( \frac{2}{12} + \frac{3}{12} + \frac{3}{12} + \frac{2}{12} + \frac{5}{12} \)
This can be concluded as the correct answer.