Solving a Tricky Math Question: Peter and Lisa's Ages

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Discussion Overview

The discussion revolves around solving a math problem involving the ages of Peter, Lisa, and their father. Participants explore the relationships between their ages through equations derived from the problem statement, which includes conditions about their combined ages and the father's age relative to Lisa's age when Peter was born.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the problem and initial equations: Peter + Lisa = 11, Peter * Lisa = Father's age, and a condition regarding the father's age when Peter was born.
  • Another participant critiques the formulation of the third equation, suggesting it misrepresents the relationship between the ages and proposes a corrected version.
  • A different participant offers their own approach, defining variables for each person's age and deriving equations, ultimately arriving at a solution for Peter and Lisa's ages.
  • One participant points out a mistake in the formulation of an equation but acknowledges that the overall solution provided is correct.
  • Another participant clarifies that the third equation can be manipulated to show equivalence with a previously suggested equation.
  • A later post reiterates the original problem statement and provides a solution, confirming the ages of Peter and Lisa and their father's age at the time of Peter's birth.

Areas of Agreement / Disagreement

There is no consensus on the formulation of the equations, with multiple participants offering different interpretations and corrections. Some participants agree on the final ages derived, while others focus on the correctness of the equations used to reach those conclusions.

Contextual Notes

Participants express uncertainty regarding the formulation of the equations and the implications of the relationships between the ages. There are unresolved aspects related to the clarity of the problem statement and the assumptions made in the equations.

Who May Find This Useful

This discussion may be useful for individuals interested in mathematical problem-solving, particularly those looking to understand age-related word problems and the formulation of equations from verbal descriptions.

amix
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Hey guys.

I have this tricky math question.

Peter and his big sister Lisa are together 11 years old. The product of their age is equal to the age of their father. When Peter was born the father was 8 times older than Lisa. How old are Lisa and Peter?

You can put up the info in the text like this:
1. Peter + Lisa = 11
2. Peter * Lisa = Fathers age
3. Fathers age = Lisa * 8

Well I have tried to solve this but without any help.

Anybody know how to do this?

Thanks.
 
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You've made a good start but the last equation is wrong.


The last sentence does not say that the father's age NOW is 8 times is 8 times Lisa's age- and that is what you are using "father's age", "Peter" and "Lisa" to represent in the first two equations.

If "Peter" is used to represent Peter's age now, then Peter was born "Peter" years ago (Yes, that looks silly- that's one reason why it's often better to use letters rather than words!).

The father's age when Peter was born was:
"father's age- Peter". At that time Lisa's age was "Lisa- Peter".
The last equation is "father- Peter= 8*(Lisa- Peter)"

Here's how I would do the problem myself:

Let P= Peter's age now, L= Lisa's age now, F= father's age now.

Then the first sentence, "Peter and his big sister Lisa are together 11 years old.", becomes the equation "P+ L= 11".

The second sentence, "The product of their age is equal to the age of their father.", becomes "L*P= F".

These two equations are exactly the same as your first two equations.

The third sentence, "When Peter was born the father was 8 times older than Lisa.", becomes "F- P= 8*(L- P)".
That last equation is equivalent to F- P= 8L- 8P which is also equivalent to F= 8L- 7P.

The first equation, P+ L= 11 is the same as L= 11- P (Subtract P from both sides).

If we replace the L in F= 8L- 7P by 11-P, we get F= 8(11-P)-7P
= 88- 8P- 7P= 88- 15P: that is, F= 88- 15P.

Now, replace F and L in L*P= F by those:

L*P= (11-P)*P= 88- 15P which is the same as
11P- P<sup>2</sup>= 88- 15P

adding P<sup>2</sup> and subtracting 11P from both sides gives

P<sup>2</sup>- 26P+ 88= 0.

That's a quadratic equation for P. You can solve that by using the quadratic equation, completing the square, or factoring (factoring is simplest IF the polynomial factors- here it DOES!).

Once you have found Peter's age (P), you can use L= 11- P to find Lisa's age and F= 88- 15P to find the father's age.

Be sure to check that your answers make the original sentences true!
 
Ok, I didn't understand the previous solution, so I'll post my own... but I've always been horrible at maths...

Peter's age - x.
Lisa's age - y.
Father's age - z.

x + y = 11
xy = z
8 (y - x) + x = z

xy = 8y - 7x
11x - x^2 (squared) = 88 - 8x - 7x
x^2 - 26x + 88 = 0
x1 = 22 (doesn't fit)
x2 = 4

y = 11 - 4 = 7
4 * 7 = z = 28

Peter's age = x = 4
Lisa's age = y = 7
Father's age = z = 28
 
Last edited:
BTW

(y - x) is the difference in age between lisa and peter
 
thanks allot guys.
I really could use you help, and I appreciate it!
 
Tail
Umm ... weird.
Your third equation is wrong, it should be :
8(y-x)=(z-x)
BUT[/B} the first line in your solution (which is supposed to be based on the second and third equations) is right, so i suppose you just made a mistake while writing the third equation.
Otherwise, your answers are right :smile:.
 
I edited the post... a little mistake, as I did the calculations on paper and then typed them...
 
Staii--- Have you been staying up too late?

Tail's "third equation" 8(y- x)+ x= z is exactly equivalent to
8(y-x)= z- x (and to my "F- P= 8*(L- P)").

True, a direct translation of the sentence gives 8(y-x)= z- x but
Tail just went ahead and added x to both sides.
 
amix said:
Hey guys.

I have this tricky math question.

Peter and his big sister Lisa are together 11 years old. The product of their age is equal to the age of their father. When Peter was born the father was 8 times older than Lisa. How old are Lisa and Peter?

You can put up the info in the text like this:
1. Peter + Lisa = 11
2. Peter * Lisa = Fathers age
3. Fathers age = Lisa * 8

Well I have tried to solve this but without any help.

Anybody know how to do this?

Thanks.

PETER is 4
LISA is 7
Their father was 24 when Peter was born, but at that time Lisa was 3.
Then 4 years later Lisa is 7 and Peter is 4.
Now since it is 4 years later their father is 28
7 times 4 is equal to 28.
 

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