Warm-Up

Chapter Test

Pg. 452

#7, 12

Homework

Questions?

Chapter 9 Extension Project

Break-Even Point

Systems with Three Variables

Objective

I want to be able to understand how to find a break-even point and solve systems with three variables.

What is a break-even point?

Bellman, Allan E., et al. Algebra 1. Bostom: Pearson Education, 2009. Print. Prentice Hall Mathematics.

Define: Let p = the number of pages.

Let d = the amount of dollars of expenses or income.

Relate: Expenses are per-page Income is price expenses plus times pages typed. computer purchase.

Write: d = 0.5 p + 1750 d = 5.5 p

Suppose you have a typing service. You buy a personal

computer for $1750 on which to do your typing. You

charge $5.50 per page for typing. Expenses are $.50 per

page for ink, paper, electricity, and other expenses. How

many pages must you type to break even?

Choose a method to solve this system. Use

substitution since it is easy to substitute for d

with these equations.

d = 0.5p + 1750 Start with one equation.

5.5p = 0.5p + 1750 Substitute 5.5p for d.

5p = 1750 Solve for p.

p = 350

To break even, you must type 350 pages.

Suppose you are starting an office-cleaning service. You have spent $315 on equipment. To clean an office, you use $4 worth of supplies. You charge $25 per office

1. Define your variables. Write a system of linear equations.

Let f = the number of offices.

Let d = the amount of dollars of expenses or income.

d = 4f + 315 d = 25f

Suppose you are starting an office-cleaning service. You have spent $315 on equipment. To clean an office, you use $4 worth of supplies. You charge $25 per office

2. How many offices must you clean to break even? Use the method of substitution.

d = 4f + 315 d = 25f

4f + 315 = 25f

315 = 21f

f = 15

15 offices must be cleaned to break even

Suppose you are starting an office-cleaning service. You have spent $315 on equipment. To clean an office, you use $4 worth of supplies. You charge $25 per office

3. How much money will you have spent when you break even?

d = 4(15) + 315 d = 25(15)

d = 375 d = 375

$375 will be spent after cleaning 15 offices. There will also be $375 for income providing the break even point (15, 375).

Suppose you are starting an office-cleaning service. You have spent $315 on equipment. To clean an office, you use $4 worth of supplies. You charge $25 per office

Graph the system of linear equations. Use your break-even point to help determine an appropriate scale so that the break-even point is centered on the graph.

Label the axes; provide an

appropriate scale. Label the income and

expenses lines. Label the break-even point.

3 6 9 12 15 18 21 24 27 0

150

350

200

250

300

100

400

450

500

Number of offices cleaned

Do

lla

rs

50

break-even point

Equations in Three Variables

Systems of equations can involve three variables.

x + y + z= 7

y + z = 6

z =4

Use substitution to solve this system of equations.

Equations in Three Variables

Begin by substitution the value of z into the second equation.

z = 4

y + (4) = 6

y = 2

Now substitute the values for y and z into the first equation.

Equations in Three Variables

y = 2, z = 4

x + 2 + 4 = 7

x = 1

The solution of the system is (1, 2, 4).

Chapter 9 Project Page # Title Personal Due Date

Cover Chapter 9 Project

1st

Project Descriptions

2nd Blogging: Emily Warren Roebling (1843-1903)

3rd Consumer Decisions

4th Equations in Three Variables

Homework:

Study for Chapter 9 Assessment

Clear your calculators! 2nd + 7 1 2 CLEAR ENTER Take out your agendas! Copy down DUE DATES!

Journal Entry On the next box (do not skip boxes) fill in the following:

– DATE

– TOPIC: Chapter 9 Project

– Answer the following question: Explain what a break-even point is in your own words.