The weight of steel varies directly with its length in feet. If a piece of steel 12 feet long weighs 168 pounds, how much will a piece of steel 20 feet long weigh? 


Since the weight of steel varies directly with its length, we can express this relationship as:

\[
W = k \cdot L
\]

Where:
- \( W \) is the weight of the steel,
- \( L \) is the length of the steel, and
- \( k \) is the constant of proportionality.

First, we need to determine \( k \). We are given that when the length is 12 feet, the weight is 168 pounds:

\[
168 = k \cdot 12
\]

Solving for \( k \):

\[
k = \frac{168}{12} = 14
\]

Now that we know \( k = 14 \), we can use this to find the weight of a piece of steel that is 20 feet long:

\[
W = 14 \cdot 20 = 280 \, \text{pounds}
\]

Therefore, a piece of steel that is 20 feet long will weigh **280 pounds**.

Would you like further details or explanations?

Here are 5 related questions:
1. What is the formula for direct variation, and how is it applied?
2. How do you calculate the constant of proportionality in a direct variation problem?
3. How would the weight change if the steel piece were 30 feet long?
4. Can direct variation be applied to other physical relationships, like speed and time?
5. What would the weight be for a piece of steel 10 feet long?

**Tip:** In direct variation problems, once the constant is found, it can be applied to any value of the variable.

The weight of steel varies directly with its length in feet. If a piece of steel 12 feet long weighs 168 pounds, how much will a piece of steel 20 feet long weigh?

Find out how to calculate the weight of a 20-foot steel piece using direct variation principles. Given that a 12-foot piece weighs 168 pounds, the problem explores proportional relationships between weight and length. Suitable for students in Grades 6-8.

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