This must be fictitious

P

Probability

Full Member
Joined
Jan 26, 2012
Messages
425
No matter how many times I read this I can't make sense of it, and even when a solution is provided I can't grasp how the author believes that the question proves the solution?

Here is the question.

Lynn is four times the age she was 63 years ago. How old is Lynn?

The solution says she is 84 years old.

In the notes to this type of question the student is advised to look out for words like; 'is', 'or was' or 'will be'. The author says this can be the equivalent of an equals sign, which makes absolutely no sense at all to me, and 63 years old is not equal to 84 years old, hence I'm lost in the understanding of this question.

What does this mean; Lynn is four times the age she was 63 years ago?

She is certainly not 252 years old otherwise our Queen would have issued her two 100th birthdays cards by now and be asking serious questions? ?
 
Well, let's start by checking the claimed answer. That can be a great way to see what a problem means.

Lynn is 84 now.​
​
How old was she 63 years ago? 84 - 63 = 21.​
​
What is 4 times her age then? 4*21 = 84.​
​
So, yes, she is (now) 4 times the age she was (then) 63 years ago.​
​
That is, her age now (84) is (=) 4 times her age then (4*21).​

Now forget that we know the answer, and do the same thinking with a variable.

There are two different ages involved here: her age now (x) and her age 63 years ago (x-63). So the equation we write is

x = 4(x - 63)​

Then you solve that.


What you need to do here is to break down the grammar of the sentence:

Lynn is four times the age she was 63 years ago.​

That is (paraphrasing, which I also find very useful),

Lynn's age now is 4 times Lynn's age 63 years ago.​

You make a variable or expression for each bold phrase, then combine them into an equation.
 
Dr.Peterson said:
Well, let's start by checking the claimed answer. That can be a great way to see what a problem means.

Lynn is 84 now.​
​
How old was she 63 years ago? 84 - 63 = 21.​
​
What is 4 times her age then? 4*21 = 84.​
​
So, yes, she is (now) 4 times the age she was (then) 63 years ago.​
​
That is, her age now (84) is (=) 4 times her age then (4*21).​

Now forget that we know the answer, and do the same thinking with a variable.

Let's forget everything above as I was given the answer to her age. Had I not have been given her age I'd not know any of the above.

There are two different ages involved here: her age now (x) and her age 63 years ago (x-63). So the equation we write is

x = 4(x - 63)​

Then you solve that.


What you need to do here is to break down the grammar of the sentence:

Lynn is four times the age she was 63 years ago.​

That is (paraphrasing, which I also find very useful),

Lynn's age now is 4 times Lynn's age 63 years ago.​

You make a variable or expression for each bold phrase, then combine them into an equation.
Click to expand...
Mathematically I can work out the solution but my concern was I can't seem to grasp the understanding from;

Lynn is four times the age she was 63 years ago.

The key parts of that statement are "Four times" and 63, hence the creating the equation;

[MATH]{a}={4}({a}-{63})[/MATH]
Mathematically doing this is one thing but seeing the understanding of it and knowing she is 84 is something else!
 
The only criticism I would have of Probability's answer is that he should have stated that
"a is Lynn's current age". Once that have been said it should be clear that "Lynn's age 63 years ago" is a- 63. Since Lynn's current age, a, is "four times Lynn's age 63 years ago", a= 4(a- 63).
 
HallsofIvy said:
The only criticism I would have of Probability's answer is that he should have stated that
"a is Lynn's current age". Once that have been said it should be clear that "Lynn's age 63 years ago" is a- 63. Since Lynn's current age, a, is "four times Lynn's age 63 years ago", a= 4(a- 63).
Click to expand...

Yes, the key to these is to clearly define the variable, in this case as "Lynn's age now".

Probability said:
Mathematically I can work out the solution but my concern was I can't seem to grasp the understanding from;

Lynn is four times the age she was 63 years ago.

The key parts of that statement are "Four times" and 63, hence the creating the equation;

[MATH]{a}={4}({a}-{63})[/MATH]
Mathematically doing this is one thing but seeing the understanding of it and knowing she is 84 is something else!
Click to expand...
Are you saying that there is still something you don't feel you understand? I can't quite follow the distinction you are making. I fully understand that the main issue can be the meaning of the statement itself, if that's part of what you mean. That was the point of my going through the check (just as paraphrasing a poem can be a way to check that you understand how the words fit together).
 
Yes I still don't fully understand the statement. The problem I seem to be having is in the understanding of "four times the age she was 63 years ago". I've been trying to look at the wording and ask myself what it means! It seems from the statement that I must understand I have to go back 63 years to find her age then before I find her age now! In the light of not knowing how old she is now the math will calculate that age and then by subtracting 63 from it I see she is 21 sixty three years ago. 4 x 21 = 84 years old now. I'm am confused with the statement even though the math works it out.
 
Probability said:
Yes I still don't fully understand the statement. The problem I seem to be having is in the understanding of "four times the age she was 63 years ago". I've been trying to look at the wording and ask myself what it means! It seems from the statement that I must understand I have to go back 63 years to find her age then before I find her age now! In the light of not knowing how old she is now the math will calculate that age and then by subtracting 63 from it I see she is 21 sixty three years ago. 4 x 21 = 84 years old now. I'm am confused with the statement even though the math works it out.
Click to expand...
It sounds like you just aren't used to puzzles, which is what this is.

Commonly, we use language to express facts directly (unless we're a politician, or a poet, or ...). Here, it's stating a fact that has to be unraveled to determine the underlying facts. But it really isn't that uncommon to have partial information, from which you have to apply reason to deduce other information; that's what science, and court cases, and many other things are about. You have to suspend your expectation that you can directly find the needed information, and accept a mindset in which you can solve a problem indirectly.
 
Just before I call it a day and put this topic bed, can I ask is this method of calculating age accurate or just a made up puzzle at the end of the day? I've done some research on it using my own age over the last 20 years and the closest I can get is 44 years old ten years ago and 60 years old today and both ages are incorrect.
 
Probability said:
Just before I call it a day and put this topic bed, can I ask is this method of calculating age accurate or just a made up puzzle at the end of the day? I've done some research on it using my own age over the last 20 years and the closest I can get is 44 years old ten years ago and 60 years old today and both ages are incorrect.
Click to expand...
This is not a method of calculating age. This is a problem (I wouldn't call it a puzzle) which describes 2 ways to relate 2 numbers and asks to find them. Did you read my previous post? Same numbers and no ages in that example.
Regarding your age, could you post complete statement of the problem you are trying to solve? You get 44 and 60, ok, but what was the question?
 
I followed the guidance of the example I originally posted. Yes I did read your example but please remember too much information can be off putting to someone trying to find their feet understanding a new topic/subject.

I've managed to do another example following the guidelines of the original wording in the question. I've used age that I know to be true and tried to establish if I can use the method of math to work out with any accuracy what the age would be in past tense, so here is that example;

I'm looking for 4 times the age 40 years ago.

[MATH]{a}=4({a}-{40})[/MATH]
[MATH]{a}={4a}-{160}[/MATH]
[MATH]{160}={4a}-{a}[/MATH]
[MATH]{a}={53}[/MATH]
[MATH]{53}-{40}={13}\times{4}={53}[/MATH]
It's not quite correct but I used rounded numbers and I'm not too sure the calculator would generate the exact right numbers anyway, but looking at unrounded numbers without say within a few months it looks reasonable. In 1982 I left school which was 38 years ago and the calculation is based on 40 years, which is not an exact science. I'm still learning...
 
I think that probability is not seeing where the line is drawn between solving specific problems and solving general problems. In the abstract, this is just a question about specific numbers. It will always be true that 4 times 21 is 84, and 21 is 63 less than 84. The relationship does not work for any other set of numbers. It does not make any difference whether the numbers refer to years or crumpets.

This is an example where the statement is much clearer in the language of mathematics. Her current age is 4 times what her age used to be 63 years ago.
 
Probability said:
I followed the guidance of the example I originally posted. Yes I did read your example but please remember too much information can be off putting to someone trying to find their feet understanding a new topic/subject.

I've managed to do another example following the guidelines of the original wording in the question. I've used age that I know to be true and tried to establish if I can use the method of math to work out with any accuracy what the age would be in past tense, so here is that example;

I'm looking for 4 times the age 40 years ago.

[MATH]{a}=4({a}-{40})[/MATH]
[MATH]{a}={4a}-{160}[/MATH]
[MATH]{160}={4a}-{a}[/MATH]
[MATH]{a}={53}[/MATH]
[MATH]{53}-{40}={13}\times{4}={53}[/MATH]
It's not quite correct but I used rounded numbers and I'm not too sure the calculator would generate the exact right numbers anyway, but looking at unrounded numbers without say within a few months it looks reasonable. In 1982 I left school which was 38 years ago and the calculation is based on 40 years, which is not an exact science. I'm still learning...
Click to expand...
It is not a general method. It is true for just one set of specific numbers.
 
I can make up another example.

Tom's age now is 5 times what his age was 56 years ago.

But that exact relationship is true just for those three numbers.
 
Probability said:
I followed the guidance of the example I originally posted. Yes I did read your example but please remember too much information can be off putting to someone trying to find their feet understanding a new topic/subject.

I've managed to do another example following the guidelines of the original wording in the question. I've used age that I know to be true and tried to establish if I can use the method of math to work out with any accuracy what the age would be in past tense, so here is that example;

I'm looking for 4 times the age 40 years ago.

[MATH]{a}=4({a}-{40})[/MATH]
[MATH]{a}={4a}-{160}[/MATH]
[MATH]{160}={4a}-{a}[/MATH]
[MATH]{a}={53}[/MATH]
[MATH]{53}-{40}={13}\times{4}={53}[/MATH]
It's not quite correct but I used rounded numbers and I'm not too sure the calculator would generate the exact right numbers anyway, but looking at unrounded numbers without say within a few months it looks reasonable. In 1982 I left school which was 38 years ago and the calculation is based on 40 years, which is not an exact science. I'm still learning...
Click to expand...
If you want to do another example start from the answer. Pick an age. Let's say 50. Pick a multiple that will be used in the problem. Let's say 5. Divide 50 by 5. Result is 10. So, the age now is 50, the age then is 10. The difference between them is 40. Now we can formulate the problem:

Joe is five times the age he was 40 years ago. How old is Joe?

And again, for the love of math, please never do stuff like this:
[MATH]{53}-{40}={13}\times{4}={53}[/MATH]The 3 expressions are not equal!
 
I'm not sure that works JeffM

[MATH]{a}={5}({a}-{56})[/MATH]
[MATH]{a}={5a}-{280}[/MATH]
[MATH]{280}={5a}-{a}[/MATH]
[MATH]\frac{280}{4}=\frac{4a}{4}[/MATH]
[MATH]{a}={70}[/MATH]
[MATH]{70}-{56}={14}\times{4}={56}[/MATH]
But we started with (5)?

All my other calculations work out using the same number and not one less?
 
lev888 said:
If you want to do another example start from the answer. Pick an age. Let's say 50. Pick a multiple that will be used in the problem. Let's say 5. Divide 50 by 5. Result is 10. So, the age now is 50, the age then is 10. The difference between them is 40. Now we can formulate the problem:

Joe is five times the age he was 40 years ago. How old is Joe?

And again, for the love of math, please never do stuff like this:
[MATH]{53}-{40}={13}\times{4}={53}[/MATH]The 3 expressions are not equal!
Click to expand...
Sorry about that I didn't think about starting a new line.
 
Probability said:
Just before I call it a day and put this topic bed, can I ask is this method of calculating age accurate or just a made up puzzle at the end of the day? I've done some research on it using my own age over the last 20 years and the closest I can get is 44 years old ten years ago and 60 years old today and both ages are incorrect.
Click to expand...

I described this sort of problem as a "puzzle" because I think that provides a useful model of what we are doing.

I just did a crossword puzzle; I was given a list of clues and a grid, and had to figure out the one set of words that would fit both the clues and the grid. They didn't say that any set of words would work, just that there is one set that I had to work out.

The other day I solved a jigsaw puzzle; I was given a pile of pieces and had to figure out where each one goes to create a coherent picture. They didn't say that any picture I wanted was in there, or that any arrangement would work, but that there is one arrangement that would make a picture.

A word problem in algebra is similar. You are given some clues (namely, that Lynn's age now is four times the age she was 63 years ago), and have to find the one age for which that is true. They don't say that this is true for anyone's age, just that there is some age for which it is true.

The difference between an algebra problem and an arithmetic problem is that in arithmetic you are given some data that you just have to combine to get a desired result (like a Lego set with instructions for building one castle by putting the pieces together in a certain order). In algebra, typically, you have to work backward to find the Lego pieces that will make that castle, so to speak.

So you can make up a problem whose answer is your own age (see post #15) and ask someone else to solve it; that becomes a way to imply your age without directly telling them. And that's because what you tell them is not true for just anyone, but is specific to you.
 
Probability said:
I'm not sure that works JeffM

[MATH]{a}={5}({a}-{56})[/MATH]
[MATH]{a}={5a}-{280}[/MATH]
[MATH]{280}={5a}-{a}[/MATH]
[MATH]\frac{280}{4}=\frac{4a}{4}[/MATH]
[MATH]{a}={70}[/MATH]
[MATH]{70}-{56}={14}\times{4}={56}[/MATH]
But we started with (5)?

All my other calculations work out using the same number and not one less?
Click to expand...
What did I say? I said Tom's age now is FIVE times what it was 56 years ago.

You compute the answer correctly as 14. You then multiply it by 4 rather than 5. Why?

5 * 14 = 70.

70 - 56 = 14.

The fact that 4 came up in the way you calculated the answer does not change the fact that the original problem specified 5. So why use 4?
 
JeffM said:
What did I say? I said Tom's age now is FIVE times what it was 56 years ago.

You compute the answer correctly as 14. You then multiply it by 4 rather than 5. Why?

5 * 14 = 70.

70 - 56 = 14.

The fact that 4 came up in the way you calculated the answer does not change the fact that the original problem specified 5. So why use 4?
Click to expand...
I've somehow misunderstood what I was doing after dividing both sides by 4. This is the point I used 4 instead of reverting back to 5.
 
You must log in or register to reply here.
Top