1. Sections 1. 4: Rewriting Equations and Formulas Section 1
Sections 1.4: Rewriting Equations and Formulas Section 1.5: Problem Solving
What you will learn:
1. How to solve for a single variable
2. How to develop an algebraic equations (or…the dreaded word problem)

2. Rewriting Formulas and Equations
Solve 7x – 3y = 8 for y
Objective: Section Rewriting Equations and Formulas, Problem Solving

3. You Try 11x – 9y = -4 solve for y
Objective: Section Rewriting Equations and Formulas, Problem Solving

4. Substituting and Solving for a Variable
Sometimes substituting values for variables is easier when you solve for a variable. For example:
Give the equation x + xy = 1, find the value of y when
x = -1 and x = 3.
Step 1: solve for y
Step 2: substitute
Objective: Section Rewriting Equations and Formulas, Problem Solving

5. You Try
Given the equation xy – x = 4, find the value of y when x = -4 and x = 2.
Step 1, solve for y
Step 2, substitute
Objective: Section Rewriting Equations and Formulas, Problem Solving

6. Word Problems
You are putting on a concert. Your goal is to sell $25,000 in tickets. You plan to charge $25.25 per adult and expect to sell 800 adult tickets. You need to determine what to charge for child tickets. How much should you charge if you plan to sell 200 child tickets? 300? 400?
R = Revenue p1 = price for adult p2 = price for child
A = number of adult tickets C = number of child tickets
Objective: Section Rewriting Equations and Formulas, Problem Solving

7. You Try
You are selling two types of caps – basic and deluxe. Write a revenue equation for this scenario.
You expect to sell 125 of the basic hats at $8.00 each. To meet your goal of $1600 in sales, what would you need to charge for the deluxe hats if you can sell 50? 60?
Objective: Section Rewriting Equations and Formulas, Problem Solving

8. Rewriting Common Formulas
The formula for perimeter is p = 2l + 2w. Solve for w.
Objective: Section Rewriting Equations and Formulas, Problem Solving

9. You Try Solve Einstein’s energy formula E = mc2 for m, mass
Objective: Section Rewriting Equations and Formulas, Problem Solving

10. Expressing One Variable in Terms of Another
Sometimes we need to express a variable in terms of another variable. Example: You have 40 feet of fencing with which to enclose a rectangular garden. Express the garden’s area in terms of its length only.
A = lw
Objective: Section Rewriting Equations and Formulas, Problem Solving

11. Algebraic Models
Verbal Model – an equation in words or…a word problem.
Algebraic Model – The word problem as a mathematical statement.
Objective: Section Rewriting Equations and Formulas, Problem Solving

12. Tons of Word Problems
The Bullet Train runs between the Japanese cities of Osaka and Fukuoka, a distance of 550 kilometers. When it makes no stops, it takes 2 hours and 15 minutes to make the trip. What is the average speed of the Bullet Train?
Distance = Rate x Time Labels
Distance = 550
Rate = r
Time = 2.25
Objective: Section Rewriting Equations and Formulas, Problem Solving

13. You Try
On August 15, 1995 the Concorde flew 35,035 mi from New York City to New York City in 31 hours, 27 minutes. What was the average speed?
Distance = Rate x Time Labels:
Objective: Section Rewriting Equations and Formulas, Problem Solving

14. Looooong Word Problems
Example 4 on page 35.
Step 1, Draw a picture:
Step 2, Verbal Model:
Step 3, Labels:
Total miles of track = Union Pacific rate = 20
Central Pacific rate = Union Pacific time = t - 24
Central Pacific time = t
Step 4, Algebraic Model:
Objective: Section Rewriting Equations and Formulas, Problem Solving

15. You Try
A fire truck is called to a scene. Three minutes later, a second truck is called. The first truck averages only 30 mph, but the second truck averages 60 mph. The trucks travel a total of 12 miles and arrive at the same time. How long from the first call did the trucks take to arrive? How far did each travel?
Verbal Model: Labels:
Algebraic Model:
Objective: Section Rewriting Equations and Formulas, Problem Solving

16. Algebraic Model from a Pattern
The table gives the heights to the top of the first few stories of a tall building. Determine the height to the top of the 15th story.
Verbal Model: Labels:
Algebraic Model:
Story
Lobby 1 2 3 4
Height to top of story in feet 20 32 44 56 68
Objective: Section Rewriting Equations and Formulas, Problem Solving

17. Using Formulas with Word Problems
A spherical weather balloon needs to hold 175 cubic feet of helium to be buoyant enough to lift an instrument package to a desired height. To the nearest tenth of a foot, what is the radius of the balloon.
Objective: Section Rewriting Equations and Formulas, Problem Solving

18. Homework Page 29, problems 14, 22, 24, 26, 28 and 30
Page 37, problems 8-11 all, 18
Quiz: Open Note
Concentrate on:
Identifying types of numbers
Identifying properties
Solving equations
Objective: Section Rewriting Equations and Formulas, Problem Solving