Substitute from Word Problems Test Prep AK

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1. (B) 22

$\eqalign{F&=9.8m\\215.6&=9.8m\\\dfrac{215.6}{9.8}&=\dfrac{9.8m}{9.8}\\22&=m}$

2. (A) 15

$\eqalign{n&=2000-5p^2\\875&=2000-5p^2\\875-2000&=2000-2000-5p^2\\-1125&=-5p^2\\\dfrac{-1125}{-5}&=\dfrac{-5p^2}{-5}\\225&=p^2\\\sqrt{225}&=\sqrt{p^2}\\15&=p}$

3. (A) 900

$\eqalign{F&=50+0.11d\\149&=50+0.11d\\149-50&=50-50+0.11d\\99&=0.11d\\\dfrac{99}{0.11}&=\dfrac{0.11d}{0.11}\\900&=d}$

4. 36

$\eqalign{A&=\dfrac{\pi}{2}\times(\dfrac{d}{2})^2\\162\pi&=\dfrac{\pi}{2}\times(\dfrac{d}{2})^2\\162\cancel{\pi}\times\dfrac{2}{\cancel{\pi}}&=\dfrac{\cancel{\pi}}{\cancel{2}}\times\dfrac{\cancel{2}}{\cancel{\pi}}\times(\dfrac{d}{2})^2\\324&=(\dfrac{d}{2})^2\\\sqrt{324}&=\sqrt{(\dfrac{d}{2})^2}\\18&=\dfrac{d}{2}\\18\times2&=\dfrac{d}{\cancel{2}}\times\cancel{2}\\36&=d}$