1. Section Formulas

2. What You Will Learn Formulas Evaluating a Formula
Solving for a Variable in a Formula

3. Definitions
A formula is an equation that typically has a real-life application.
To evaluate a formula, substitute the given values for their respective variables and then evaluate using the order of operations.

4. Example 1: Simple Interest
The simple interest formula,
interest = principal × rate × time,
or i = prt,
is used to find the interest you must pay on a simple interest loan when you borrow principal, p, at simple interest rate, r, in decimal form, for time, t.

5. Example 1: Simple Interest
Chris Campbell borrows $5000 at a simple interest rate of 6.5% for 3 years.
a) How much will Chris Campbell pay in interest at the end of 3 years?
b) What is the total amount he will repay the bank at the end of 3 years?

6. Example 1: Simple Interest
a) How much will Chris Campbell pay in interest at the end of 3 years?
Solution
p = $5000, r = 6.5%, t = 3
Chris must pay $975 in interest.

7. Example 1: Simple Interest
What is the total amount he will repay the bank at the end of 3 years?
Solution
The total he must pay at the end of 3 years is the principal, $5000, plus the $975 interest, for a total of $5975.

8. Example 2: Volume of an Ice-Cream Box
The formula for the volume of a rectangular box is
volume = length × width × height,
or V = lwh.
Use the formula V = lwh to find the width of a rectangular box of ice cream if l =7 in., h =3.5 in., and V =122.5 in3.

9. Example 2: Volume of an Ice-Cream Box
l =7 in., h =3.5 in., and V =122.5 in3
Solution
The width of the ice-cream box is 5 in.

10. Mathematical Models
When we represent real phenomena, such as finding simple interest, mathematically we say we have created a mathematical model or simply a model to represent the situation. A model may be a single formula, an equation, or a system of many equations.

11. μ (mu), σ (sigma), Σ (capital sigma), δ (delta), Δ (capital delta),
Greek Letters
Many formulas contain Greek letters, such as
μ (mu),
σ (sigma),
Σ (capital sigma),
δ (delta),
Δ (capital delta),
ε (epsilon),
π (pi),
θ (theta), and
λ (lambda).

12. Example 3: A Statistics Formula
A formula used in the study of statistics to find a standard score (or z-score) is
Find the value of z. when = 120,
μ = 100, σ = 16, n = 4.

13. Example 3: A Statistics Formula
Solution
= 120, μ = 100, σ = 16, n = 4.

14. Subscripts Some formulas contain subscripts.
Subscripts are numbers (or letters) placed below and to the right of variables.
For example, if two different amounts are used in a problem, they may be symbolized as A and A0 (read “A sub zero” ), or A1 (read “A sub one”) and A2 (read “A sub two”).

15. Solving for a Variable in a Formula or Equation
You are given a formula or an equation expressed in terms of one variable and asked to express it in terms of a different variable.
To do so, treat each of the variables, except the one you are solving for, as if it were a constant.
Then solve for the variable desired.

16. Example 4: Solving for a Variable in an Equation
Solve the equation 2x + 5y –10 = 0 for y.
Solution

17. Example 4: Solving for a Variable in an Equation
Solution

18. Example 4: Solving for a Variable in an Equation
Solution
The equation is solved for y:
The solution can also be expressed in the form
This form is convenient for graphing linear equations.

19. Example 5: Solving for a Variable in a Formula
An important formula used in statistics is
Solve this equation for x.

20. Example 5: Solving for a Variable in a Formula
Solution or