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The weight of a certain wire is 145 pounds per 1,000 feet. What is the cost of 600 feet of this wire at $1.40 per 100 pounds?

Answer :

To find the cost of 600 feet of the wire, we’ll break the problem into steps:

1. Determine the weight of 600 feet of wire:
- We know the wire weighs 145 pounds per 1,000 feet.
- To determine the weight for just 600 feet, we calculate the proportion of 600 to 1,000 feet and multiply by the known weight for 1,000 feet.
- Formula:
[tex]\[
\text{Weight of 600 feet} = \left( \frac{600}{1000} \right) \times 145
\][/tex]
- Solving this gives us a weight of 87 pounds.

2. Calculate the cost for 87 pounds of wire:
- The cost is [tex]$1.40 per 100 pounds.
- To find the cost for 87 pounds, we need to determine how many "hundreds of pounds" are in 87 pounds:
\[
\text{Cost of 87 pounds} = \left( \frac{87}{100} \right) \times 1.40
\]
- Solving this provides a cost of $[/tex]1.218.

Therefore, the weight of the 600 feet of wire is 87 pounds, and the cost is $1.218.

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