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Answer :
Sure, let's work through the problem step by step!
1. Understand the problem:
We need to find the cost of 600 feet of wire, knowing that the wire weighs 145 pounds per 1,000 feet and costs [tex]$1.40 per 100 pounds.
2. Calculate the weight of 600 feet of wire:
- The wire weighs 145 pounds for every 1,000 feet.
- First, we find out how much it weighs per foot by dividing:
\[
\text{Weight per foot} = \frac{145 \text{ pounds}}{1000 \text{ feet}} = 0.145 \text{ pounds per foot}
\]
- Now, calculate the total weight for 600 feet:
\[
\text{Weight of 600 feet} = 0.145 \text{ pounds/foot} \times 600 \text{ feet} = 87 \text{ pounds}
\]
3. Calculate the cost of 87 pounds of wire:
- The cost is $[/tex]1.40 for every 100 pounds.
- First, find out the cost per pound:
[tex]\[
\text{Cost per pound} = \frac{1.40 \text{ dollars}}{100 \text{ pounds}} = 0.014 \text{ dollars per pound}
\][/tex]
- Now, calculate the total cost for 87 pounds:
[tex]\[
\text{Total cost} = 87 \text{ pounds} \times 0.014 \text{ dollars/pound} = 1.218 \text{ dollars}
\][/tex]
4. Round the total cost:
- Round [tex]$1.218 to $[/tex]1.22 to get it to two decimal places.
Therefore, the cost of 600 feet of this wire is $1.22.
1. Understand the problem:
We need to find the cost of 600 feet of wire, knowing that the wire weighs 145 pounds per 1,000 feet and costs [tex]$1.40 per 100 pounds.
2. Calculate the weight of 600 feet of wire:
- The wire weighs 145 pounds for every 1,000 feet.
- First, we find out how much it weighs per foot by dividing:
\[
\text{Weight per foot} = \frac{145 \text{ pounds}}{1000 \text{ feet}} = 0.145 \text{ pounds per foot}
\]
- Now, calculate the total weight for 600 feet:
\[
\text{Weight of 600 feet} = 0.145 \text{ pounds/foot} \times 600 \text{ feet} = 87 \text{ pounds}
\]
3. Calculate the cost of 87 pounds of wire:
- The cost is $[/tex]1.40 for every 100 pounds.
- First, find out the cost per pound:
[tex]\[
\text{Cost per pound} = \frac{1.40 \text{ dollars}}{100 \text{ pounds}} = 0.014 \text{ dollars per pound}
\][/tex]
- Now, calculate the total cost for 87 pounds:
[tex]\[
\text{Total cost} = 87 \text{ pounds} \times 0.014 \text{ dollars/pound} = 1.218 \text{ dollars}
\][/tex]
4. Round the total cost:
- Round [tex]$1.218 to $[/tex]1.22 to get it to two decimal places.
Therefore, the cost of 600 feet of this wire is $1.22.
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