To find the total weight of the suitcases, we need to add the weights:
-
Convert all weights to improper fractions:
- \( 24 \frac{1}{2} = \frac{24 \times 2 + 1}{2} = \frac{49}{2} \)
- \( 13 \frac{3}{8} = \frac{13 \times 8 + 3}{8} = \frac{107}{8} \)
- \( 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \)
- \( 17 \frac{3}{4} = \frac{17 \times 4 + 3}{4} = \frac{71}{4} \)
Now we have:
- \( 24 \frac{1}{2} = \frac{49}{2} \)
- \( 13 \frac{3}{8} = \frac{107}{8} \)
- \( 3 \frac{1}{2} = \frac{7}{2} \)
- \( 17 \frac{3}{4} = \frac{71}{4} \)
- Find a common denominator:
The least common multiple of 2, 8, and 4 is 8. We can rewrite each fraction with a denominator of 8:
- \( \frac{49}{2} = \frac{49 \times 4}{2 \times 4} = \frac{196}{8} \)
- \( \frac{107}{8} \) is already in terms of eighths.
- \( \frac{7}{2} = \frac{7 \times 4}{2 \times 4} = \frac{28}{8} \)
- \( \frac{71}{4} = \frac{71 \times 2}{4 \times 2} = \frac{142}{8} \)
Now we have:
- \( \frac{196}{8} \)
- \( \frac{107}{8} \)
- \( \frac{28}{8} \)
- \( \frac{142}{8} \)
- Add the fractions:
\[ \frac{196}{8} + \frac{107}{8} + \frac{28}{8} + \frac{142}{8} = \frac{196 + 107 + 28 + 142}{8} \]
Calculating the numerator: \[ 196 + 107 = 303 \] \[ 303 + 28 = 331 \] \[ 331 + 142 = 473 \]
So: \[ \frac{473}{8} \]
- Convert the improper fraction back to a mixed number:
To convert \( \frac{473}{8} \) to a mixed number, divide 473 by 8: \[ 473 \div 8 = 59 \quad \text{(remainder } 1\text{)} \]
Thus, \( 473 = 8 \times 59 + 1 \), so we have: \[ \frac{473}{8} = 59 \frac{1}{8} \]
- Final result: Converting back, we see that \( 59 \frac{1}{8} \) is equivalent to \( 59 + \frac{1}{8} = 59 + 0.125 = 59.125 \).
Since the answer options are:
- A) \( \frac{588}{8} \) (which equals 73.5 and is not among our results),
- B) \( 69 \frac{3}{8} \),
- C) \( 85 \frac{1}{8} \),
- D) \( 71 \frac{1}{8} \),
The closest match is NOT found, but calculating clearly suggests the total weight of the luggage is not represented in the options given. However, with my calculation confirming that the total weight is \( 59 \frac{1}{8} \) lb (approximately 59.125 lb).
Since this total doesn't match any of the proposed answers outright, I'm concluding this is incorrect or might be a misprint in options offered.
Nonetheless, the total weight of all the luggage is:
\(\text{Total Weight} = 59 \frac{1}{8} lb\).