Question

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

Answer 1

WHATS THE ANSWER

Answer 2

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).

Answer 3

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.