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# Algebra "Age Problem"

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On this Presentation, you will learn how to solve some age problems, and there are exercise in the end of the presentation. So i hope that you'll learn mo about Problem solving and you'll explore yourself to know this section

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• Thank you :) Big Help

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• Manuel Alvarez is ten times older than his son,Andrew. In 20 years, Manuel's age will be 4 more than twice Andrew's age. How old was he when Andrew was born?

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• y u should use (x+29)? it is stated in the problem that ' he will be twice as old as his son's age', so if his son's age at that time will be (x+8);where x=present age and plus 8 for the coming 8 yrs. Therefore it should be 2(x+8) instead of 2 (x+29). Am I right?

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• WHY IS IT SON X AND ALVIN IS ALSO X ALVIN SHOULD B Y RIGHT..?ITHINK YOUR WRONG ABOUT YOUR EQUATION..

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### Algebra "Age Problem"

1. 1. Using Equations in Solving Age Problem e-math Elementary Algebra By: Karla Mae S. Glavez SPCP
2. 2. <ul><li>• In dealing with age problems, it is important to keep in mind that the ages of different people change at the same rate. For example, after two years, all the people in the given problem are two years older than they were two years ago. Four years ago, all the people in the problem were four years younger. </li></ul>
3. 3. <ul><li>• Also, it is easier if one makes a table showing the representation for current ages in the problem, “future” ages (a number of years from now), and “past” ages ( a number of years ago). </li></ul>
4. 4. <ul><li>• If possible, represent the youngest present age by a single letter, then represent the other ages. This process is illustrated in the following examples. </li></ul><ul><li>example: </li></ul><ul><li>Next. . . </li></ul>
5. 5. example 1 <ul><li>EXAMPLE 1 : </li></ul><ul><li>Alvin is now 21 years older than his son. In 8 years, he will be twice as old as his son’s age. What are their present ages? </li></ul><ul><li>SOLUTION: </li></ul><ul><li>READ: Reading the problem thoroughly, we fin a relationship between the present ages of Alvin and his son and the relationship of their ages 8 years from now. </li></ul>
6. 6. <ul><li>REPRESENT: Using the relationship between the present ages, we have </li></ul><ul><li>Let x = the son’s present age </li></ul><ul><li>RELATE: Then, x + 21 = Alvin’s present age </li></ul><ul><li>After 8 years, each age is increasen by 8: x + 8 and x + 29 as given </li></ul>
7. 7. EQUATE: Using the vsecong relationship: In 8 years, Alvin’s age is twice his son’s age, we have x + 29 = 2 ( x + 8) SOLVE: Manipulating the equation, we have x + 29 = 2(x + 8) x + 29 = 2x + 16 x = 13 x + 29 x + 21 Alvin x + 8 x son FUTURE ( 8 YEARS FROM NOW) NOW
8. 8. <ul><li>ANSWERS: x = 13 son’s age </li></ul><ul><li>x + 21 = 13 + 21 = 34 Alvin’s age </li></ul><ul><li>PROOF: Alvin’s age is 21 years more than his son’s age: 34 = 13 + 21. </li></ul><ul><li>In 8 years: </li></ul><ul><li> son: 13 + 8 = 21 </li></ul><ul><li> Alvin: 29 + 13 = 42 </li></ul><ul><li> Alvin’s age is twice his son’s age: </li></ul><ul><li> 42 = 2 (21) </li></ul><ul><li>42 = 42 </li></ul>
9. 9. Example 2 <ul><li>The sum of Patrick’s age and Marko’s age is 58. Eight years ago, Patrick was twice as old as Marko then. How old is Marko? </li></ul><ul><li>SOLUTION: </li></ul><ul><li>READ: We find that we have a relationship between their present ages and their ages 8 years ago. </li></ul><ul><li>REPRESENT: Let x = Marko’s present age </li></ul>
10. 10. <ul><li>RELATE: Then 58 – x = Patrick’s present age </li></ul><ul><li> We subtract 8 years from each as shown in the table below. </li></ul>50 - x 58 - x Patrick x - 8 x Mako Past ( 8 Years Ago) NOW
11. 11. <ul><li>EQUATE: The second relationship gives us our equation: Eight years ago, Patrick was twice as old as Marko then. </li></ul><ul><li> 50 – x = 2(x – 8) </li></ul><ul><li>SOLVE: Manipulating the equation, we have: </li></ul><ul><li> 50 – x = 2(x – 8) </li></ul><ul><li> 50 – x = 2x – 16 </li></ul><ul><li> 3x = 66 </li></ul><ul><li> x = 22 </li></ul><ul><li>ANSWERS: x = 22 Marko’s age </li></ul><ul><li> 58 – x = 36 Patrick’s age </li></ul>
12. 12. <ul><li>PROOF: The sum of their ages is 58: Marko’s age = 22 </li></ul><ul><li>Patrick’s age = 36 </li></ul><ul><li>Add 58 </li></ul><ul><li>Eight years ago, Patrick was twice as old as Marko then: </li></ul><ul><li>36 – 8 = 2(22 – 8) </li></ul><ul><li> 28 = 2(14) </li></ul><ul><li> 28 = 28 </li></ul>
13. 13. Example 3 <ul><li>Aries is twice as old as Rico while Jake is 24 years younger than Aris. If half of Aries’ age six years ago was three less than one-half the sum of Rico’s age in four years and Jake’s present age, find the ages of each. </li></ul><ul><li>SOLUTION: </li></ul><ul><li>Let x = Rico’s present age </li></ul><ul><li>Then 2x = Aries’ present age </li></ul><ul><li>And 2x – 24 = Jake’s present age </li></ul>
14. 14. Half of Aries’ age 6 years ago was 3 les than one-half the sum of Rico’s age in 4 years and Jake’s present age: ½ (2x – 6) = ½ [(x + 4) + (2x – 24)] – 3 2x -6 = x + 4 + 2x – 24 -6 2x – 6 = 3x -26 x = 20 2x – 20 2x – 30 2x - 24 Jake 2x + 4 2x – 6 2x Aries x + 4 x – 6 x Rico Future ( Years From Now) Past (6 Years Ago) Now
15. 15. <ul><li>ANSWERS: x = 20 Rico’s age </li></ul><ul><li>2x = 40 Aires’ age </li></ul><ul><li>2x – 24 = 16 Jake’s age </li></ul><ul><li>PROOF: Arie’s is twice as old as Rico: 40 = 2(20) </li></ul><ul><li>40 = 40 </li></ul><ul><li> Jake’s is 24 years younger than Aries: 16 = 40 -24 </li></ul><ul><li>16 = 16 </li></ul><ul><li> Half of Aries’ age 6 years ago was 3 less than one-half the sum of Rico’s age in 4 years and Jakes present age: </li></ul><ul><li>½ (34) = ½ (24 + 16) -3 </li></ul><ul><li>17 = 20 – 3 </li></ul><ul><li>17 = 17 </li></ul>
16. 16. Example 4 <ul><li>Mrs. Canteno is 40 years old and her eldest daughter is 12. When will the mother be twice as old as her eldest daughter? </li></ul><ul><li>SOLUTION: </li></ul><ul><li>Let x = the number of years that mother will be twice as old as her eldest daughter. </li></ul><ul><li>Then 40 + x = mother’s age in x years. </li></ul><ul><li>And 12 + x = daughter’s age in x years </li></ul>
17. 17. Mother will be twice as old as her eldest daughter: 40 + x = 2(12 + x ) 40 + x = 24 + 2x Proof: Mother’s age in 16 years: 40 + 16 = 56 Daughter’s age in 16 years: 12 + 16 = 28 56 = 2 (28) 56 = 56 12 + x 12 Daughter 40 + x 40 Mother FUTURE ( X YEARS FROM NOW) Now
18. 18. EXERCISES: 1.) Mercy is 17 years old now. Represent her age – a. 2 years from now c. x years from now e. x + 7 years hence b. 3 years ago d. 2x years ago 2.) Melchor is m years old now. Represent his age – a. 15 years from now c. a years ago e. 5x years from now b. 11 years ago d. n + 5 years ago 3.) Mr. Matthew Matics is y + 5 years old now. Represent his age – a. 3 years ago d. 5y years from now b. 8 years from now e. 3y – 5 years from now c. 2y + 3 years ago 4.) In 4 years, Mr5. Parabola will be 17 years old. Represent his age – a. now c. 6 years from now e. a – 3 from now b. 8 years ago d. x years ago
19. 19. 5.) Arielle will be 57 years old p years from now. Represent her age – a. now c. 4 years from now e. m years ago b. 3 years ago d. m years from now 6.) Five years ago, Edwin was 27 years old. Represent his age – a. at present c. 5 years from now e. q years from now b. 3 years from now d. q years ago 7.) P years ago, Mr. Reyes was Q years old. Represent his age – a. at present c. 5 years ago e. P + 4 years ago b. 2 years from now d. R years from now
20. 20. ANSWERS <ul><li>1.) C. </li></ul><ul><li>2.) C. </li></ul><ul><li>3.) D. </li></ul><ul><li>4.) B. </li></ul><ul><li>5.) D. </li></ul><ul><li>6.) C. </li></ul><ul><li>7.) D. </li></ul>
21. 21. Solve each of the following <ul><li>1.) Mr. Reyes is 25 years older than his son. How old are the father and the son if Mr. Reyes is 5 more then thrice as old as his son? </li></ul>