To determine the total cost to carpet Jean's room, follow these steps:

Step 1: Convert room dimensions from feet to yards

Since the carpet cost is given per square yard, we first need to convert the dimensions of the room from feet to yards.

1 yard = 3 feet, so:

• The length of the room in yards: $\frac{13}{3} \approx 4.33 \, \text{yards}$
• The width of the room in yards: $\frac{11}{3} \approx 3.67 \, \text{yards}$

Step 2: Calculate the area of the room in square yards

The area $A$ of the room in square yards is calculated by multiplying the length and the width in yards: $A = 4.33 \, \text{yards} \times 3.67 \, \text{yards} \approx 15.89 \, \text{square yards}$

Step 3: Calculate the total cost

The cost per square yard of the carpet is $29.85. Therefore, the total cost to carpet the room is: $\text{Total cost} = 15.89 \, \text{square yards} \times 29.85 \, \text{dollars per square yard}$

Let's calculate that.

$\text{Total cost} \approx 15.89 \times 29.85 = 474.43 \, \text{dollars}$

Final Answer:

Jean's total cost to carpet her room is approximately $474.43.

Would you like more details, or do you have any questions?

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Here are five related questions for you:

1. How would the cost change if the carpet price increased to $32 per square yard?
2. What if the room's dimensions were 15 feet by 12 feet?
3. How much would it cost if Jean only carpeted half of the room?
4. How do you convert other measurements from feet to yards for irregularly shaped rooms?
5. What is the total area in square feet, and how does it compare to square yards?

Tip: Always make sure to convert the units appropriately when dealing with different systems, like feet and yards, for more accurate results.