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You and your friends have packed four suitcases for the trip. The weights of the suitcases are 24 1/2 lb, 13 3/8 lb, 31/2 lb, and 17 3/4 lb

. What is the total weight of all the luggage?(2 points)
Responses

A 588/8 lb

B 69 3/8 lb

C 85 1/8 lb

D 71 1/8 lb

PLEASE WRITE YOUR WORK

3 answers

To find the total weight of the suitcases, we need to add up all of their individual weights.

Let's write down the weights:

  1. \( 24 \frac{1}{2} \) lb
  2. \( 13 \frac{3}{8} \) lb
  3. \( 3 \frac{1}{2} \) lb
  4. \( 17 \frac{3}{4} \) lb

Before adding, it can be easier to convert all mixed numbers to improper fractions.

Step 1: Convert mixed numbers to improper fractions

  1. \( 24 \frac{1}{2} = 24 + \frac{1}{2} = \frac{49}{2} \)

  2. \( 13 \frac{3}{8} = 13 + \frac{3}{8} = \frac{107}{8} \)

  3. \( 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{7}{2} \)

  4. \( 17 \frac{3}{4} = 17 + \frac{3}{4} = \frac{71}{4} \)

Step 2: Find a common denominator

The denominators are 2, 8, and 4. The least common multiple (LCM) of these denominators is 8.

Now we’ll convert each of the improper fractions to have a denominator of 8:

  1. \( \frac{49}{2} = \frac{49 \times 4}{2 \times 4} = \frac{196}{8} \)

  2. \( \frac{107}{8} = \frac{107}{8} \) (stays the same)

  3. \( \frac{7}{2} = \frac{7 \times 4}{2 \times 4} = \frac{28}{8} \)

  4. \( \frac{71}{4} = \frac{71 \times 2}{4 \times 2} = \frac{142}{8} \)

Step 3: Add the fractions

Now we can add all these fractions together: \[ \frac{196}{8} + \frac{107}{8} + \frac{28}{8} + \frac{142}{8} = \frac{196 + 107 + 28 + 142}{8} \]

Calculating the numerator: \[ 196 + 107 = 303 \] \[ 303 + 28 = 331 \] \[ 331 + 142 = 473 \]

Thus, we have: \[ \frac{473}{8} \]

Step 4: Convert the improper fraction back to a mixed number

To convert \( \frac{473}{8} \) to a mixed number:

  1. Divide 473 by 8:
    • \( 473 \div 8 = 59 \) remainder \( 1 \)

Thus, we have: \[ \frac{473}{8} = 59 \frac{1}{8} \]

Final conversion to decimal

Now, since \( 59 \frac{1}{8} = 59 + 0.125 \), we convert to a decimal: \[ 59 + 0.125 = 59.125 \]

Compare with the answers

The choices given in the problem are:

  • A. \( \frac{588}{8} \) (which corresponds to 73.5)
  • B. \( 69 \frac{3}{8} \) (which is 69.375)
  • C. \( 85 \frac{1}{8} \) (which is 85.125)
  • D. \( 71 \frac{1}{8} \) (which is 71.125)

Since: \[ \frac{473}{8} = 59 \frac{1}{8} = 59.125 \]

None of the answers match 59.125, indicating a possible error in the original set of choices or weights provided. The calculation appears correct, so the correct answer is:

\( 59 \frac{1}{8} \) lb or \( \frac{473}{8} \) (which is not in the provided options).

WHATS THE ANSWER

I apologize for any confusion. Let's carefully calculate the total weight again for clarity.

Weights to add:

  1. \( 24 \frac{1}{2} \) lb
  2. \( 13 \frac{3}{8} \) lb
  3. \( 3 \frac{1}{2} \) lb
  4. \( 17 \frac{3}{4} \) lb

Step 1: Convert mixed numbers to improper fractions

  1. Convert \( 24 \frac{1}{2} \): \[ 24 \frac{1}{2} = 24 + \frac{1}{2} = \frac{49}{2} \]

  2. Convert \( 13 \frac{3}{8} \): \[ 13 \frac{3}{8} = 13 + \frac{3}{8} = \frac{107}{8} \]

  3. Convert \( 3 \frac{1}{2} \): \[ 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{7}{2} \]

  4. Convert \( 17 \frac{3}{4} \): \[ 17 \frac{3}{4} = 17 + \frac{3}{4} = \frac{71}{4} \]

Step 2: Find a common denominator

The least common multiple of the denominators 2, 8, and 4 is 8.

So, we convert all fractions to have a denominator of 8:

  1. \(\frac{49}{2} = \frac{49 \times 4}{2 \times 4} = \frac{196}{8}\)
  2. \(\frac{107}{8} = \frac{107}{8}\) (remains the same)
  3. \(\frac{7}{2} = \frac{7 \times 4}{2 \times 4} = \frac{28}{8}\)
  4. \(\frac{71}{4} = \frac{71 \times 2}{4 \times 2} = \frac{142}{8}\)

Step 3: Add the fractions

Now we add all these 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, we have: \[ \frac{473}{8} \]

Step 4: Convert to a mixed number

Now, dividing \( 473 \) by \( 8 \):

  • \( 473 \div 8 = 59 \) with a remainder of \( 1 \).

This means: \[ \frac{473}{8} = 59 \frac{1}{8} \]

The answer \( 59 \frac{1}{8} = 59.125 \) is not among the choices you provided.

Choices Given:

  • A: \( \frac{588}{8} \)
  • B: \( 69 \frac{3}{8} \)
  • C: \( 85 \frac{1}{8} \)
  • D: \( 71 \frac{1}{8} \)

Conclusion

Given the calculation, none of the options match \( 59 \frac{1}{8} \).

However, if we have to choose the closest option from the provided responses, we observed that the options don't seem to match our total weight clearly.

Thus the total luggage weight is indeed:

59 \(\frac{1}{8}\) lb.

If forced to select from the options provided, none would be correct. Please double-check the weights given or consider that there might be an issue with the choices listed.