Problem
Name 凹 Chapter 7 Review/Test Personal Math Trainer Online Assessment and Intervention 1. Mrs. Williams is organizing her office supplies. There are 3 open boxes of paper clips in her desk drawer. Each box has \( \frac{7}{8} \) of the paper clips remaining. How many boxes of paper clips are left? Shade the model and complete the calculations below to show how you found your answer. full boxes of paper clips 2. Diana worked on her science project for \( 5 \frac{1}{3} \) hours. Gabe worked on his science project \( 1 \frac{1}{4} \) times as long as Diana. Paula worked on her science project \( \frac{3}{4} \) times as long as Diana. For 2a-2d, select True or False for each statement. 2a. Diana worked longer on her science project than Gabe worked on his science project. True False 2b. Paula worked less on her science project than Diana worked on her science project. True False 2c. Gabe worked longer on his science project than Paula worked on her science project. True False 2d. Gabe worked longer on his science project than Diana and Paula combined. True False 3. GODEEPER Louis wants to carpet the rectangular floor of his basement. The basement has an area of 864 square feet. The width of the basement is \( \frac{2}{3} \) its length. What is the length of Louis's basement? feet
Solution
Step 1 ：\[\text{1. Calculate total paper clips:}\]
Step 2 ：\[3 \times \frac{7}{8} = \frac{21}{8}\]
Step 3 ：\[\text{2a. Calculate Gabe's work time:}\]
Step 4 ：\[5 \frac{1}{3} \times \frac{5}{4} = \frac{16}{3} \times \frac{5}{4} = \frac{80}{12} = 6 \frac{2}{3}\]
Step 5 ：\[\text{2b-c. Calculate Paula's work time:}\]
Step 6 ：\[5 \frac{1}{3} \times \frac{3}{4} = \frac{16}{3} \times \frac{3}{4} = \frac{48}{12} = 4\]
Step 7 ：\[\text{3. Calculate basement length (L) and width (W):}\]
Step 8 ：\[\text{Area = Length (L) x Width (W), with } W = \frac{2}{3}L \text{, so:}\]
Step 9 ：\[864 = L \times \left(\frac{2}{3}L\right)\]
Step 10 ：\[L^2 = \frac{3}{2} \times 864\]
Step 11 ：\[L^2 = 1296 \Rightarrow L = \sqrt{1296} \Rightarrow L = 36\]
