Cutting paper

Jodi is cutting out pieces of paper that measure 8 1/2 inches by 11 inches from a larger sheet of paper that has an area of 1,000 square inches.
What is the area of each piece of paper that Jodi is cutting out?

Final Answer:

A =  93 ¹⁄₂ = 187/2 in²
B =  65 in²

Step-by-step explanation:

$$\begin{gathered} a=8\frac{1}{2}=8+\frac{1}{2}=\frac{8\cdot 2+1}{2}=\frac{16+1}{2}=\frac{17}{2}=8.5\text{in} \\ b=11\text{in} \\ A=a\cdot b=\frac{17}{2}\cdot 11=\frac{17\cdot 11}{2}=\frac{187}{2}=\frac{187}{2}{\text{in}}^2=93\frac{1}{2}{\text{in}}^2=93.5{\text{in}}^2 \end{gathered}$$

$$\begin{gathered} S=1000{\text{in}}^2 \\ n=\lfloor S/A\rfloor =\lfloor 1000/93.5\rfloor =10 \\ B=S-n\cdot A=1000-10\cdot \frac{187}{2}=65{\text{in}}^2 \end{gathered}$$

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