![SOLUTION
Solve:
Manipulating the equation, we have
[3(x+2x)]+[x]+[2x]+[3(x+2x)+2x]
3x+6x + x + 2x + 3x+6x+2x
23x
(1/23) 23x
x
=
=
=
=
=
69
69
69
(1/23) 69
3](https://image.slidesharecdn.com/ageproblem-140217025707-phpapp01/85/Math-Sample-Age-Problem-7-320.jpg)
![PROOF
From the given statement: My mother whose
age is the total of all our ages is now 69, we
have
Mr. Santillana + wife + son + daughter
= mother
[3(x+2x)] + x + 2x + [3(x+2x)+2x] = 69
{3[3+2(3)]}+(3)+2(3)+{3[3+2(3)]+2(3)} = 69
[3 (3+6)] + 3 + 6 + [3 (3+6) +6] = 69
3(9) + 9 + 3(9) + 6 = 69
27+9+27+6 = 69
69 = 69](https://image.slidesharecdn.com/ageproblem-140217025707-phpapp01/85/Math-Sample-Age-Problem-9-320.jpg)
Math Sample Age Problem
- 2. PROBLEM Mr. Santillana, a mathematics teacher was travelling by bus with his family consisting of his mother, wife, son, and daughter. The bus conductor doubting the girl’s right to have a half-fare ticket asked, “How old is your daugHter?” Mr. Santillana, irritated at having his honesty questioned, confused the conductor with his answer: “My
- 3. SOLUTION Read: Reading the problem thoroughly, we find a relationship between the present ages of Mr. Santillana, his mother, wife, son and daughter.
- 4. SOLUTION Represent: Using the relationship between their present ages, we have Let x = the son’s present age
- 6. SOLUTION Equate: Using the relationship: My mother whose age is the total of all our ages is now 69, we have Mr. Santillana + wife + son + daughter = mother
- 7. SOLUTION Solve: Manipulating the equation, we have [3(x+2x)]+[x]+[2x]+[3(x+2x)+2x] 3x+6x + x + 2x + 3x+6x+2x 23x (1/23) 23x x = = = = = 69 69 69 (1/23) 69 3
- 8. ANSWERS Daughter’s age: 2x = 2(3) ; x=3 = 6 Thus, Mr. Santillana’s daughter is 6 years old.
- 9. PROOF From the given statement: My mother whose age is the total of all our ages is now 69, we have Mr. Santillana + wife + son + daughter = mother [3(x+2x)] + x + 2x + [3(x+2x)+2x] = 69 {3[3+2(3)]}+(3)+2(3)+{3[3+2(3)]+2(3)} = 69 [3 (3+6)] + 3 + 6 + [3 (3+6) +6] = 69 3(9) + 9 + 3(9) + 6 = 69 27+9+27+6 = 69 69 = 69