# 1.5 – Solving Literal Equations and Formulas

Objectives

• Solve literal equations with two variables.
• Rearrange formulas to solve for a quantity of interest in a real-world problem.
• Describe the steps in solving equations.
• Use units to guide and interpret your solutions of literal equations and formulas.

Key Terms

• Formula – an equation that describes an important mathematical relationship.
• Literal Equation – an equation that involves two or more variables.

Notes

• If you have two variables, you can solve for either one of them using reverse operations, even without having a value to substitute
• Example:  Fahrenheit and Celsius are ways to tell the temperature.  In the USA, we use Fahrenheit.  In Europe, they use Celsius.
• Here is the formula for finding Celsius:
• $C=\frac{5}{9}(F-32)$
• What if you wanted to solve for Fahrenheit instead?  Try solving for F by doing inverse (reverse) operations until you isolate the F.
• Step 1: Multiply by 9 on both sides
• $9C=9*\frac{5}{9}(F-32)$ and this will give you:  $9C=5(F-32)$
• Step 2: Divide by 5 on both sides
• $\frac{9}{5}C=5\frac{(F-32)}{5}$ and this will give you: $\frac{9}{5}C=F-32$
• Step 3: Add 32 to both sides
• You get the formula for finding Fahrenheit:  $\frac{9}{5}C+32=F$
• If you want, you can rewrite it as $F=\frac{9}{5}C+32$

• Example: Substitution
• Find x when y = 6 in the literal equation 5x + 4y = 39
• Step 1: Write with substitution: 5x + 4(6) = 39
• Step 2: Simplify: 5x + 24 = 39
• Step 3: Isolate the variable by subtracting 24 from both sides, THEN by dividing by 5 on both sides.
• Question: Maya is taking her friends to a concert. Each ticket costs $25, and souvenir T-shirts are$12 each. There is a $4 service fee for the entire purchase. She has$130. If she buys 3 tickets, how many T-shirts can she buy?
• Take notes on what you have:  Tickets: $25, T-Shirts:$12, Service Fee (one time) $4, Total Budget$130