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Answer :
To find out how many pounds a barrel of 500 bolts weighs when each bolt weighs [tex]\( \frac{41}{8} \)[/tex] ounces, we will go through the following steps:
1. Determine the weight of a single bolt in ounces.
Each bolt weighs [tex]\( \frac{41}{8} \)[/tex] ounces.
2. Calculate the total weight of 500 bolts in ounces.
Multiply the weight of one bolt by the total number of bolts:
[tex]\[
\text{Total weight in ounces} = \frac{41}{8} \times 500
\][/tex]
3. Convert the total weight from ounces to pounds.
We know that 16 ounces make up 1 pound. Therefore, to convert ounces to pounds, we must:
- Divide the total ounces by 16 to find the number of pounds.
- The whole number from the division will be the pounds.
- The remainder will be in ounces.
4. Perform the calculations:
- Calculate the total weight in ounces [tex]\( \frac{41}{8} \times 500 = 2562.5 \)[/tex] ounces.
- Convert ounces into pounds and remaining ounces:
[tex]\[
\text{Pounds} = \left\lfloor \frac{2562.5}{16} \right\rfloor = 160 \text{ pounds}
\][/tex]
[tex]\[
\text{Remaining ounces} = 2562.5 \mod 16 = 2.5 \text{ ounces}
\][/tex]
So, the barrel of 500 bolts weighs 160 pounds and 2.5 ounces.
Referring back to the possible choices, none of the options directly match the result of 160 pounds and 2.5 ounces since the closest choice available in the problem does not fit exactly with our calculations. Therefore, there seems to be a discrepancy, as the weight calculated does not correspond exactly to any choices given.
1. Determine the weight of a single bolt in ounces.
Each bolt weighs [tex]\( \frac{41}{8} \)[/tex] ounces.
2. Calculate the total weight of 500 bolts in ounces.
Multiply the weight of one bolt by the total number of bolts:
[tex]\[
\text{Total weight in ounces} = \frac{41}{8} \times 500
\][/tex]
3. Convert the total weight from ounces to pounds.
We know that 16 ounces make up 1 pound. Therefore, to convert ounces to pounds, we must:
- Divide the total ounces by 16 to find the number of pounds.
- The whole number from the division will be the pounds.
- The remainder will be in ounces.
4. Perform the calculations:
- Calculate the total weight in ounces [tex]\( \frac{41}{8} \times 500 = 2562.5 \)[/tex] ounces.
- Convert ounces into pounds and remaining ounces:
[tex]\[
\text{Pounds} = \left\lfloor \frac{2562.5}{16} \right\rfloor = 160 \text{ pounds}
\][/tex]
[tex]\[
\text{Remaining ounces} = 2562.5 \mod 16 = 2.5 \text{ ounces}
\][/tex]
So, the barrel of 500 bolts weighs 160 pounds and 2.5 ounces.
Referring back to the possible choices, none of the options directly match the result of 160 pounds and 2.5 ounces since the closest choice available in the problem does not fit exactly with our calculations. Therefore, there seems to be a discrepancy, as the weight calculated does not correspond exactly to any choices given.
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