b. Nicholas's mother plans to carpet his bedroom. The floor measures \( 12 \frac{2}{3} \mathrm{ft} \). by \( 14 \frac{1}{2} \mathrm{ft} \). The carpet she wants costs \( \$ 5.25 \) per square foot. How many square feet must she buy and what will be the cost

To determine how many square feet of carpet Nicholas's mother needs to buy and the total cost, follow these steps: ### 1. Calculate the Area of the Bedroom **Given Dimensions:** - Length = \( 12 \frac{2}{3} \) feet - Width = \( 14 \frac{1}{2} \) feet **Convert Mixed Numbers to Improper Fractions:** - \( 12 \frac{2}{3} = \frac{38}{3} \) feet - \( 14 \frac{1}{2} = \frac{29}{2} \) feet **Calculate Area:** \[ \text{Area} = \frac{38}{3} \times \frac{29}{2} = \frac{38 \times 29}{3 \times 2} = \frac{1102}{6} \approx 183.67 \text{ square feet} \] ### 2. Determine the Total Cost **Cost per Square Foot:** \[ \$5.25 \text{ per square foot} \] **Calculate Total Cost:** \[ \text{Total Cost} = 183.67 \times 5.25 \approx \$964.25 \] ### **Final Answer:** - **Square Feet Needed:** Approximately **183.67 square feet** - **Total Cost:** **\$964.25** --- **Note:** Since carpet is typically sold by whole square feet, Nicholas's mother might consider purchasing **184 square feet** to ensure complete coverage, which would slightly increase the total cost to: \[ 184 \times \$5.25 = \$966.00 \] However, based on the exact measurements, **183.67 square feet** costing **\$964.25** is the precise requirement.