Questions: The floor of a rectangular meeting room has a raised platform that is the same length as the room and is 1/6 the width of the room. Part A What is the width of the raised platform? Write an equation to model your work. Part B Estimate the area of the floor, including the raised platform.

Solution Steps

• The length of the room is \(7 \frac{1}{3}\) yards.
• The width of the room is \(6 \frac{2}{5}\) yards.

• The raised platform is \(\frac{1}{6}\) of the width of the room.
• Convert the width of the room to an improper fraction: \(6 \frac{2}{5} = \frac{32}{5}\).
• Calculate \(\frac{1}{6}\) of \(\frac{32}{5}\): \[ \frac{1}{6} \times \frac{32}{5} = \frac{32}{30} = \frac{16}{15} \]

• The area of the floor is the product of the length and width of the room.
• Convert the length of the room to an improper fraction: \(7 \frac{1}{3} = \frac{22}{3}\).
• Calculate the area: \[ \text{Area} = \frac{22}{3} \times \frac{32}{5} = \frac{704}{15} \approx 46.93 \text{ square yards} \]

Final Answer