Practice Solving Literal Equations

1. The following formula gives the temperature's measure in degrees Fahrenheit F, where ‍C is the measure in degrees Celsius:

   $$F=\frac{9}{5}C+32$$

   Rearrange the formula to highlight the measure in degrees Celsius.

2. The following formula is used in economics to find a factory's unit labor cost ‍U, where ‍O is the hourly output per worker and ‍W is the hourly compensation per worker.

   $$U = \frac{W}{O}$$

   Rearrange the formula to highlight the hourly output per worker.

3. The following formula gives the area ‍A of a trapezoid, where ‍b and ‍c are the bases of the trapezoid and ‍h is the height:

   $$A=\frac{1}{2}(b+c)h$$

   Rearrange the formula to highlight the height.

4. The following formula gives an object's average speed ‍S, where ‍T is the time it takes the object to travel a distance ‍D.

   $$S=\frac{D}{T}$$

   Rearrange the formula to highlight time.

Source: Khan Academy, https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:modeling/x2ec2f6f830c9fb89:manipulating-formulas/e/manipulating-formulas
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Formulas may contain multiple variables, along with known numbers and letters that stand for known constants like ‍$$\pi$$.

We can highlight a certain variable in the formula by treating the formula as an equation where we want to solve for that variable.

1. In this case, we need to solve the equation $$F=\frac{9}{5}C+32$$ for C.

   $$F=\frac{9}{5}C+32$$

   $$F-32=\frac{9}{5}C$$

   $$\frac{5}{9} \cdot (F-32)$$
   

   This is the result of rearranging the formula to highlight the measure in degrees Celsius:

   $$C=\frac{5}{9} \cdot (F-32)$$

2. In this case, we need to solve the equation $$U=\frac{W}{O}$$ for O.

   $$U=\frac{W}{O}$$

   $$U \cdot =W$$

   $$O=\frac{W}{U}$$

   This is the result of rearranging the formula to highlight the hourly output per worker:
   

   $$O=\frac{W}{U}$$

3. In this case, we need to solve the equation

   $$A=\frac{1}{2}(b+c)h$$ for h.

   $$A=\frac{1}{2}(b+c)h$$

   $$\frac{2A}{b+c}=h$$

   This is the result of rearranging the formula to highlight the height:

   $$h=\frac{2A}{b+c}$$

4. In this case, we need to solve the equation $$S = \frac{D}{T}$$ for T.

   $$S = \frac{D}{T}$$

   $$S \cdot T = D$$

   $$T = \frac{D}{S}$$

   This is the result of rearranging the formula to highlight time:

   $$T = \frac{D}{S}$$