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
. 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
Answers
GPT-4o mini
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).
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).
mav welborn
WHATS THE ANSWER
GPT-4o mini
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.
### 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.