1. § 3.2 Solving Application Problems

2. Angel, Elementary Algebra, 7ed 2 Problem Solving 1.Understand the problem. Identify the quantity or quantities you are being asked to find. 2.Translate the problem into an equation. a.) Choose a variable to represent one quantity and write down what it represent. Represent any other quantity to be found in terms of this variable. b.) Using the information from step a), write an equation that represents the application.

3. Angel, Elementary Algebra, 7ed 3 Problem Solving 3.Carry out the mathematical calculations necessary to solve the problem. 4.Check the answer (using the original application). 5.Answer the question asked.

4. Angel, Elementary Algebra, 7ed 4 Solving Equations Example: With the AT&T calling plan, you pay $4.95 a month plus 7 cents per of talk time. In a specific month, the total cost for the monthly fee and talk time was $29.45. Determine the number of minutes of talk time. Let t = the number of minutes of talk time Monthly charge = 4.95 +.07 for each minute used Continued.

5. Angel, Elementary Algebra, 7ed 5 Solving Equations Monthly charge = 4.95 +.07 for each minute used 29.45 = 4.95 +.07t Solve the equation. 29.45 = 4.95 +.07t 24.50 =.07t 350 = t There were 350 minutes of talk time. Check: 4.95 +.07(350) = 4.95 + 24.5 = 29.45 Example continued:

6. Angel, Elementary Algebra, 7ed 6 Solving Equations Example: At a 1-day 20% off sale, Kathy purchased a hat for $25.99. What is the regular price of the hat? Let h = the regular price of the hat sale price = original price - 20% of original price 25.99 = h - 0.2h Solve the equation. Continued.

7. Angel, Elementary Algebra, 7ed 7 Solving Equations 25.99 = h - 0.2h 25.99 = 0.8h (Remember that h = 1h.) 32.49 = h The original price of the hat was $32.49. Check: 32.49 – 0.2(32.49) = 32.49 – 6.50 = 25.99 Example continued: