- Represent the relationship between the width \(W\) and length \(L\) of the table as \(\frac{L}{3} = W\).
- Substitute the given width \(W = 6\) into the equation to get \(\frac{L}{3} = 6\).
- Multiply both sides by \(3\) to find the length: \(L = 18\) feet.
- Select the matching option: \(\boxed{\frac{L}{3} = 6; L = 18 \text{ feet}}\).
Explanation
- Problem Analysis and Formulation
We are given that the width of the table is \(W = 6\) feet and that the width is a third of its length \(L\). We can translate this relationship into a mathematical equation:
\[W = \frac{1}{3}L\]
Or equivalently:
\[\frac{L}{3} = W\]
Our goal is to write this equation using the given width and then solve it for the unknown length \(L\).
- Solving the Equation
Since we know the width \(W = 6\) feet, we can substitute this value directly into the equation \(\frac{L}{3} = W\):
\[\frac{L}{3} = 6\]
To solve for \(L\), we multiply both sides of the equation by \(3\):
\[L = 6 \times 3\]
\[L = 18\]
Thus, the length of the table is \(18\) feet.
- Final Conclusion and Selection
Comparing our derived equation \(\frac{L}{3} = 6\) and our solution \(L = 18\) feet with the provided options, we can see that the first option matches our findings perfectly:
- \(\frac{L}{3} = 6; L = 18\) feet
- \(3L = 6; L = 2\) feet
- \(3 + L = 6; L = 3\) feet
- \(L - 3 = 6; L = 9\) feet
The correct choice is the first one.
Examples
Understanding how to translate word problems into algebraic equations is a foundational skill in many fields. For example, if you are planning to build a rectangular vegetable garden, you might decide that your garden should be twice as long as it is wide. If you know you have enough space for a width of 4 meters, you would set up the equation \(\frac{L}{2} = 4\) to find that you need 8 meters of length. This helps you plan your materials and space efficiently!