Age Word Problems

Students will solve age word problems with a Guess & Check

Table and Algebra

What’s Involved in an Age Problem

PAST PRESENT FUTURE

AGES

Solving Age ProblemsGUESS & CHECK CHARTConsiderations: Past, Present, or FutureMake a Guess and Check ChartFind the relationship between the ages.Start Guessing until the Relationship Works!Answer question

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)

Now Future (+18) Relationship: Future

B P BF PF BF = 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

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: FutureFuture (+18)Now

B

(3P)

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

(3P)

P BF PF BF = 2(PF)

54 18 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

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)

Now Future (+18) Relationship: Future

B

(3P)

P BF PF BF = 2(PF)

3X X 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.

Algebra

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

Now Past (- 15) Equation: Past

F(3S) S FP SP FP = 9 (SP)

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

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 -3x

-15 = 6x - 135

+135 +135

120 = 6x x = 20 3x = 60Son is 20 and Father is 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!!!!!