2. Age Word Problems Students will solve age word problems with a Guess & Check Table and Algebra

3. What’s Involved in an Age Problem

4. Solving Age Problems GUESS & CHECK CHART Considerations: Past, Present, or Future Make a Guess and Check Chart Find the relationship between the ages. Start Guessing until the Relationship Works! Answer question

5. What column should be your guess column? Pietro: Because Bill is three times as old as Pietro. (If I know Pietro, I can find Bill) NowFuture (+18)Relationship: Future BPBFPFBF = 2(PF) Bill is three times as old as Pietro. Eighteen years from now, Bill will be twice as old as Pietro will be then. Find present age of Bill and Pietro

6. Start Guessing Guess Column 72=2(36) 72=72 36721854 54=2(30) 54=60 30541236 48=2(28) 48=56 28481030 BF = 2(PF)PFBFP Relationship: Future Future (+18)Now B (3P)

7. Bill is three times as old as Pietro. Eighteen years from now, Bill will be twice as old as Pietro will be then. Find present age of Bill and Pietro NowFuture (+18)Relationship: Future B (3P) PBFPFBF = 2(PF) 54187236 72=2(36) 72=72 Answer the question: We need their NOW ages. Bill is 54 and Pietro is 18.

8. Solving Algebraically Plug x into Guess Column and fill in row of Guess and Check Chart Define variables Use equation from chart and solve it Answer question

9. X goes in guess column: Fill in rest of row Bill is three times as old as Pietro. Eighteen years from now, Bill will be twice as old as Pietro will be then. Find present age of Bill and Pietro 3x+18=2(x+18) X+183X+18X3X 72=2(36) 72=72 36721854 Relationship: Future Future (+18)Now BF = 2(PF)PFBFPB (3P)

10. NowFuture (+18)Relationship: Future B (3P) PBFPFBF = 2(PF) 3XX3X+18X+18 3x+18=2(x+18) Let x= Pietro Now Let 3x = Bill now Let x + 18= Pietro Future Let 3x + 18 = Bill Future 3x + 18 = 2(x + 18) 3x + 18 = 2x + 36 -2x x + 18 = 36 x = 18 Pietro is 18 and Bill is 54. Algebra

11. A father is 3 times as old as his son. Fifteen years ago, the father was 9 times as old as his son. Find their present ages. Make a Guess & Check Chart Which is the Guess Column? Son Now NowPast (- 15)Equation: Past F(3S)SFPSPFP = 9 (SP)

12. The father is 60 and the son is 20. Remember: You need 3 guesses even if you guess right early!!!!! 60=9(10)10602575 45 = 9(5) 5452060 33 = 9(1)1331648 FP = 9 (SP)SPFPSF(3S) Equation: PastPast (- 15)Now

13. 3x-15=9(x-15)X-153x-15x3x FP = 9 (SP)SPFPSF(3S) Equation: PastPast (- 15)Now Let x = Son Now Let 3x = Father Now Let x - 15 = Son Past Let 3x-15 = Father Past 3x - 15 = 9(x - 15) 3x - 15 = 9x - 135 -3x -15 = 6x - 135 +135 120 = 6x x = 20 3x = 60 Son is 20 and Father is 60

14. Wrapping Up Age Problems What are three possible time periods in age problems? Where do you put the x in the Guess & Check Chart What is the most important step? Past, Present (NOW), Future The Guess Column Answering the Question!!!!!