Fowler Erickson
09/11/2023 · Middle School

3. A store sells rope by the meter. The equation \( p=0.8 L \) represents the price \( p \) (in dollars) of a piece of nylon rope that is \( L \) meters long. a. How much does the nylon rope cost per meter? b. How long is a piece of nylon rope that costs \( \$ 1.00 \) ?

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To solve the problem, we will analyze the equation \( p = 0.8L \). ### a. How much does the nylon rope cost per meter? The equation \( p = 0.8L \) indicates that the price \( p \) is directly proportional to the length \( L \) of the rope. The coefficient of \( L \) (which is 0.8) represents the cost per meter. Thus, the cost of the nylon rope per meter is **$0.80**. ### b. How long is a piece of nylon rope that costs \( \$ 1.00 \)? To find the length \( L \) of the rope that costs \( \$ 1.00 \), we can substitute \( p = 1.00 \) into the equation and solve for \( L \): \[ 1.00 = 0.8L \] Now, we can solve for \( L \): \[ L = \frac{1.00}{0.8} = 1.25 \] Thus, a piece of nylon rope that costs \( \$ 1.00 \) is **1.25 meters long**.

Quick Answer

a. The cost per meter is $0.80. b. A rope that costs $1.00 is 1.25 meters long.
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