1. Problem
#1
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

5. SOLUTION
Relate:
PRESENT AGE
MOTHER
69
WIFE
3(x+2x)
SON
X
DAUGHTER
2x
MR. SANTILLANA
3(x+2x)+2x

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

10. -ENDBY:
APRIL LLANO
BEED 3A