Substitute from Word Problems Practice AK

1.

$\eqalign{m&=1.50p\\900&=1.50p\\\dfrac{900}{1.50}&=\dfrac{1.50p}{1.50}\\600&=p}$
2.

$\eqalign{A&=\dfrac{I}{60}\\32&=\dfrac{I}{60}\\32\times60&=\dfrac{I}{60}\times60\\1920&=I}$

3.

$\eqalign{c&=3m+9\\360&=3m+9\\360-9&=3m+9-9\\351&=3m\\\dfrac{351}{3}&=\dfrac{3m}{3}\\117&=m}$.

4.

$\eqalign{F&=\dfrac{9}{5}C + 32\\68&=\dfrac{9}{5}C + 32\\68-32&=\dfrac{9}{5}C + 32-32\\36&=\dfrac{9}{5}C\\36\times\dfrac{5}{9}&=\dfrac{9}{5}C\times\dfrac{5}{9}\\20&=C}$

5.

$\eqalign{F&=\dfrac{9}{5}C + 32\\23&=\dfrac{9}{5}C + 32\\23-32&=\dfrac{9}{5}C + 32-32\\-9&=\dfrac{9}{5}C\\-9\times\dfrac{5}{9}&=\dfrac{9}{5}C\times\dfrac{5}{9}\\-5&=C}$

6.

$\eqalign{(F-32)\times\dfrac{5}{9}&=C\\(F-32)\times\dfrac{5}{9}&=-15\\(F-32)\times\dfrac{5}{9}\times\dfrac{9}{5}&=-15\times\dfrac{9}{5}\\F-32&=-27\\F-32+32&=-27+32\\F&=5}$

7.

$\eqalign{(F-32)\times\dfrac{5}{9}&=C\\(F-32)\times\dfrac{5}{9}&=40\\(F-32)\times\dfrac{5}{9}\times\dfrac{9}{5}&=40\times\dfrac{9}{5}\\F-32&=72\\F-32+32&=72+32\\F&=104}$

8.

$\eqalign{p&=\sqrt{n-2}+9\\13&=\sqrt{n-2}+9\\13-9&=\sqrt{n-2}+9-9\\4&=\sqrt{n-2}\\4^2&=\sqrt{n-2}^2\\16&=n-2\\16+2&=n-2+2\\18&=n}$

9.

$\eqalign{(p-9)^2+2&=n\\(p-9)^2+2&=123\\(p-9)^2+2-2&=123-2\\(p-9)^2&=121\\\sqrt{(p-9)^2}&=\sqrt{121}\\p-9&=11\\p-9+9&=11+9\\p=20}$.

10.

$\eqalign{r&= \dfrac{\pi}{180} \times d\\\dfrac{3\pi}{4}&= \dfrac{\pi}{180} \times d\\\dfrac{3\pi}{4}\times\dfrac{180}{\pi}&= \dfrac{\pi}{180}\times\dfrac{180}{\pi} \times d\\135&=d}$

11.

$\eqalign{r&= \dfrac{\pi}{180} \times d\\\dfrac{10\pi}{3}&= \dfrac{\pi}{180} \times d\\\dfrac{10\pi}{3}\times\dfrac{180}{\pi}&= \dfrac{\pi}{180}\times\dfrac{180}{\pi} \times d\\600&=d}$

12.

$\eqalign{d&= \dfrac{180}{\pi}\times r\\315&= \dfrac{180}{\pi} \times r\\315\times\dfrac{\pi}{180}&= \dfrac{180}{\pi}\times\dfrac{\pi}{180} \times r\\\dfrac{7\pi}{4}&=r}$

13.

$\eqalign{d&= \dfrac{180}{\pi}\times r\\5&= \dfrac{180}{\pi} \times r\\5\times\dfrac{\pi}{180}&= \dfrac{180}{\pi}\times\dfrac{\pi}{180} \times r\\\dfrac{\pi}{36}&=r}$