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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Step-by-step Solution
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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