Copyright 2010 Pearson Education Inc All rights reserved

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 2. 2 - 1

Chapter 2 Linear Equations and Applications Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 2. 2 - 2

2. 2 Formulas and Percent Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 2. 2 - 3

2. 2 Formulas and Percent Objectives 1. Solve a formula for a specified variable. 2. Solve applied problems using formulas. 3. Solve percent problems. 4. Solve problems involving percent increase or decrease. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 4

2. 2 Formulas and Percent A Mathematical Model A mathematical model is an equation or inequality that describes a real situation. Models for many applied problems already exist and are called formulas. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 5

2. 2 Formulas and Percent A Formula A formula is a mathematical equation in which variables are used to describe a relationship. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 6

2. 2 Formulas and Percent Using formulas to describe a relationship Relationship Mathematical Formula Perimeter of a triangle: a c h Area of a triangle: b Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 7

2. 2 Formulas and Percent Using variables to describe a relationship Relationship Mathematical Formulae Volume of a cone: h Surface area of a cone: r Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 8

2. 2 Formulas and Percent Using variables to describe a relationship Relationship Celsius Fahrenheit Mathematical Formulae Celsius to Fahrenheit: Fahrenheit to Celsius: Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 9

2. 2 Formulas and Percent Using variables to describe a relationship Relationship Mathematical Formula Percent Acid, P: Acid Base Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 10

2. 2 Formulas and Percent Solving a Formula for a Specified Variable Sometimes the formula is solved for a different variable than the one to be found. One mathematical model tell us that voltage, V, in a circuit is equal to current, I, times resistance, R. V=IR To determine the amount of resistance in a circuit, it would help to first solve the formula for R. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 11

2. 2 Formulas and Percent Solving a Formula for a Specified Variable Solve the formula V = IR for R. We solve this formula for R by treating V and I as constants (having fixed values) and treating R as the only variable. Begin by writing the formula so that the variable for which we are solving, R, is on the left side. IR=V Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 12

2. 2 Formulas and Percent Solving a Formula for a Specified Variable Finally, we use the properties of the previous section to isolate the variable R. IR = V I I R = V I Divide by I. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 13

2. 2 Formulas and Percent Solving a Formula for a Specified Variable Solve the formula P = a + b + c for b. We solve this formula for b by treating P, a and c as constants (having fixed values) and treating b as the only variable. Begin by writing the formula so that the variable for which we are solving, b, is on the left side. a+b+c=P Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 14

2. 2 Formulas and Percent Solving a Formula for a Specified Variable We now solve for b. a+b+c=P a + b + c + (–a) = P + (–a) b+c=P–a b + c + (–c) = P – a + (–c) b=P–a–c Copyright © 2010 Pearson Education, Inc. All rights reserved. Add. Prop. of Eq. Sec 2. 2 - 15

2. 2 Formulas and Percent Solving a Formula for a Specified Variable b h B This formula gives the relationship between the height, h, and two bases, B and b, of a trapezoid and its area, A. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 16

2. 2 Formulas and Percent Solving a Formula for a Specified Variable Mult. Prop. of Equality. Assoc. Prop. Inverse Prop. Identity Prop. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 17

2. 2 Formulas and Percent Solving a Formula for a Specified Variable Distributive Prop. Add. Prop. of Equality. Inverse Prop. Divide by h. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 18

2. 2 Formulas and Percent Solving Applied Problems Using Formulas The volume of a triangular cylinder is given by: h l b If the volume of a triangular cylinder is 880 cm 3, the base is 10 cm, and the length is 22 cm, find the height. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 19

2. 2 Formulas and Percent Solving Applied Problems Using Formulas Continued. First, solve the equation Copyright © 2010 Pearson Education, Inc. All rights reserved. for h. Sec 2. 2 - 20

2. 2 Formulas and Percent Solving Applied Problems Using Formulas Continued. Second, find the height, h, by substituting the given values of V, b, and l into this formula: The height of the triangular cylinder is 8 cm. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 21

2. 2 Formulas and Percent Solving Percent Problems The word “percent” means per 100. For example, 5 percent means 5 per one hundred. Percent is written with the % symbol (e. g. , 5%). Let a represent the partial amount of b, the base, or whole amount. The following formula can be used to solve percent problems. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 22

2. 2 Formulas and Percent Solving Percent Problems A chain saw requires 4 ounces of a certain oil to be mixed with 60 ounces of gasoline. What is the percent of oil in the mixture? The whole amount of the mixture will be: Oil 4 ounces Let x represent the percent of oil in the mixture. Then the percent of oil in the mixture is: Gas 60 ounces Total 64 ounces Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 23

2. 2 Formulas and Percent Interpreting Percents from a Graph A 16% F 8% D 12% B 28% C 36% The pie chart shown below represents the distribution of grades in Analytic Geometry 122 last year. Use the information in the chart to estimate how many B’s will be given in a new class of size 70 students. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 24

2. 2 Formulas and Percent Interpreting Percents from a Graph A 16% F 8% According to the chart, 28% of the students should get a grade of B. Let x represent the number of students getting a B. D 12% B 28% C 36% Thus, about 20 students will get a B. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 25

2. 2 Formulas and Percent Solving Problems About Percent Increase or Decrease A hardware store marked up a water heater from their cost of $600 to a selling price of $708. What was the percent markup? The water heater was marked up 18%. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 2. 2 - 26