Age Word Problems
Students will solve age word
problems with a Guess & Check
Table and Algebra
What’s Involved in an Age
Problem
AGES
PAST
PRESENT
FUTURE
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
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
Now
B
P
Future (+18) Relationship: Future
BF
PF
BF = 2(PF)
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)
Start Guessing
Now
B
P
(3P)
30
10
Future (+18) Relationship: Future
BF PF
BF = 2(PF)
48
28
36
12
54
30
54
18
72
36
Guess Column
48=2(28)
48=56
54=2(30)
54=60
72=2(36)
72=72
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
Now
B
P
(3P)
54
18
Future (+18) Relationship: Future
BF PF
BF = 2(PF)
72
36
72=2(36)
72=72
Answer the question: We need their NOW ages.
Bill is 54 and Pietro is 18.
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
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
Now
Future (+18)
Relationship:
Future
B
P
BF
PF
BF = 2(PF)
(3P)
72=2(36)
54
18 72
36
72=72
3X
X
3X+18
X+18 3x+18=2(x+18)
X goes in guess column: Fill in rest of row
Algebra
Now
B
P
(3P)
3X X
Future (+18)
BF
PF
Relationship:
Future
BF = 2(PF)
3X+18 X+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
-2x
x + 18 = 36
x = 18
Pietro is 18
and Bill is 54.
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
Now
Past (- 15)
Equation: Past
F(3S) S
FP
FP = 9 (SP)
SP
Which is the Guess Column?
Son Now
Now
Past (- 15)
Equation: Past
F(3S) S
FP
SP
FP = 9 (SP)
48
16
33
1
33 = 9(1)
60
20
45
5
45 = 9(5)
75
25
60
10
60=9(10)
The father is 60 and the son is 20.
Remember: You need 3 guesses even if you guess
right early!!!!!
Now
Past (- 15)
Equation: Past
F(3S) S
FP
FP = 9 (SP)
3x
3x-15 X-15 3x-15=9(x-15)
x
SP
Let x = Son Now
Let 3x = Father Now
Let x - 15 = Son Past
Let 3x-15 = Father
Past
3x - 15 = 9(x - 15)
Son is 20 and Father is
60
120 = 6x
3x - 15 = 9x - 135
-3x
-3x
-15 = 6x - 135
+135
+135
x = 20 3x = 60
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!!!!!