Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 2 Equations, Inequalities and Problem Solving

22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 1. Solve for V. 2. Solve for V. 3. Solve for h. 4. Solve for h. Bellwork: V = G(N – R)

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 2.7 Percent, Ratio, and Proportion

44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Objectives:  Solve percent equations  Solve problems involving percents  Solve proportions  Solve problems modeled by proportions

55 Strategy for Problem Solving General Strategy for Problem Solving 1.UNDERSTAND the problem. Read and reread the problem. Choose a variable to represent the unknown. Construct a drawing. 2.TRANSLATE the problem into an equation. 3.SOLVE the equation. 4.INTERPRET the result: Check proposed solution in problem. State your conclusion.

66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving a Percent Problem A percent problem has three different parts: 1. When we do not know the amount: n = 10% · 500 Any one of the three quantities may be unknown. amount = percent · base 2. When we do not know the base: 50 = 10% · n 3. When we do not know the percent: 50 = n · 500

77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving a Percent Problem: Amount Unknown What is 9% of 65? 5.85 is 9% of 65 Example:

88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving a Percent Problem: Base Unknown 36 is 6% of what? 36 is 6% of 600 Example:

99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving a Percent Problem: Percent Unknown 24 is what percent of 144? Example:

10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving Markup Problems Mark is taking Peggy out to dinner. He has $66 to spend. If he wants to tip the server 20%, how much can he afford to spend on the meal? Let n = the cost of the meal. Cost of meal n+tip of 20% of the cost=$66 100% of n+20% of n=$66 120% of n=$66 Mark and Peggy can spend up to $55 on the meal itself. Example:

11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving Discount Problems Julie bought a leather sofa that was on sale for 35% off the original price of $1200. What was the discount? How much did Julie pay for the sofa? Julie paid $780 for the sofa. Discount = discount rate  list price = 35%  1200 = 420 The discount was $420. Amount paid = list price – discount = 1200 – 420 = 780 Example:

12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving Increase Problems The cost of a certain car increased from $16,000 last year to $17,280 this year. What was the percent of increase? Amount of increase = original amount – new amount The car’s cost increased by 8%. = 17,280 – 16,000 Example: = 1280

13 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Solving Decrease Problems Patrick weighed 285 pounds two years ago. After dieting, he reduced his weight to 171 pounds. What was the percent of decrease in his weight? Amount of decrease = original amount – new amount Patrick’s weight decreased by 40%. = 285 – 171 Example: = 114

14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Proportions The ratio of a number a to a number b is their quotient. A proportion is a mathematical statement that two ratios are equal. Examples

15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Cross Products If, then ad = bc. **This is cross-multiplication** **This is how we solve a proportion** means ad = bc

16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Solve for x: a)b)

17 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example To estimate the number of people in Jackson, population 50,000, who have no health insurance, 250 people were polled. Of those polled, 39 had no insurance. How many people in the city might we expect to be uninsured? 39 out of 250 uninsured How many out of 50,000?

18 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Which is a better buy for the same brand of toothpaste? 8 ounces for $2.59 or 10 ounces for $3.11 **Find the unit price, which is price divided by quantity** 32¢ per oz or 31¢ per oz

19 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Closure: 1. What is a proportion? 2. How do we solve/simplify proportional equations?