Hamster cage

Ryan keeps his hamster cage on his dresser. The area of the top of Ryan's dresser is 1 2/3 as large as the area of the bottom of his hamster cage. The area of the dresser top is 960 square inches. How many square inches of his dresser top are not covered by the hamster cage?

Correct answer:

x =  640 sq inch

Step-by-step explanation:

$$\begin{gathered} S_1=960{\text{in}}^2 \\ k=1\frac{2}{3}=1+\frac{2}{3}=\frac{1\cdot 3+2}{3}=\frac{3+2}{3}=\frac{5}{3}\doteq 1.6667 \\ {S}_2=k\cdot S_1=\frac{5}{3}\cdot 960=\frac{5\cdot 960}{3}=\frac{4800}{3}=1600 \\ x=S_2-S_1=1600-960=640\text{sq}\text{inch} \end{gathered}$$

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