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Topic: Oh, Maths!

https://www.mirror.co.uk/news/weird-new … s-29121698

I tried the problem and I got the answer.

But the method they give seems a strange way to solve it.

I started by considering that he had £x to start.

Then I produced an equation.

Multiply each term by a well-known whole number suitable for the purpose, then one finds x.

Then remember which value is wanted as the answer.

Frankly, the tone of the article implying that Mr Sunak has the wrong policy backfires. It seems to me that the tone of the article implies that Mr Sunak knows what is needed!

William

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Re: Oh, Maths!

William wrote:

Multiply each term by a well-known whole number suitable for the purpose, then one finds x.

I’m not sure what you mean by “a well-known whole number suitable for the purpose”, William. When I read that he was left with half of the amount that he started with, I was immediately prompted to think of the amount that he gave his brother (1/3 of the original sum) as being 2/3 of the half that he was left with. The amount that he spent on a present was the remaining 1/3 of the half (or 1/6 of the whole) and from there the calculation of the original sum is pretty straightforward.

“Within you, there is a stillness and a sanctuary to which you can retreat at any time and be yourself.”
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Re: Oh, Maths!

What I actually did, as mental algebra, was to start with considering that he had £x at first.

So he gave his brother £x/3

He spent £12

What he had left was £x/2

So the gift and the spend together are also £x/2.

So

x/2 - 12 + x/3

To get rid of the fractions, multiply all through bu 6.

3x = 72 + 2x

3x - 2x = 72

x=72

The required answer is x/3,

So the answer is that he gave his brother £24.

Now, I suppose in retrospect it would have been more elegant to have as the equation

x = x/3 + 12 + x/2

6x = 2x + 72 + 3x

6x -2x -3x = 72

x = 72

So x/3 is 24

So the answer is that he gave his brother £24

The web page way of doing it, namely

> So, if Hasim gave his brother 1/3 of the money, spent £12, and still has half of his money left, then: 12 = (1/6)x. You'll then need to resolve x: x = 72. 72/3 = £24, meaning this is the amount he gave his brother.

is correct, but not the way I solved it.

I ask myself 'why?'.

I suspect because the way that I did it is more straightforwardly extensible if he had also given a sixth of the original to his cousin, and a twelfth of the original to his great aunt and he still had a quarter of his original money after his generosity. smile

William

4 Reply by GB

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Re: Oh, Maths!

2/3 * x - 12 = 1/2 * x
therefore (2/3 - 1/2)x = 12
hence 1/6 * x = 12
so 1/3 * x = 24 (given to brother)

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Re: Oh, Maths!

That is an interesting way to solve the problem, working out on a rolling basis what he still has got, then forming an equation by having that what he has still got is equal to half of what he had at the start.

Rather than my approach of adding up what he has given away and spent.

William

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Re: Oh, Maths!

Geoff’s method is the same as mine, but expressed more formally.

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Re: Oh, Maths!

Geoff effectively has the man start off with x.

Then the man gives his brother some money, so has 2/3 of x remaining in his possession.

Then the man spends £12.

So what the man has left in his possession is 2/3 of x less £12.

Then that is an equal amount to what the man has left in his possession.

So two sides of an equation.

So then calculate x as a number, then calculate x/3 for the required answer.

However Alfred regards the amount that the man gave to his brother as being (of the same value as) 2/3 of the half that the man had after the gift giving and after the spend and proceeds from there.

So Alfred brought the result after the spend into the solution sequence before the spend occurred, whereas Geoff did not do that.

So to me it seems not the same method.

William

8 Reply by GB

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Re: Oh, Maths!

I'm not sure if I could have solved the problem when I was 10. It's pretty basic algebra, but I don't think I got on to algebra in junior school, and had only just got started on it in Grammar school at 10.

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Re: Oh, Maths!

I was not taught algebra at primary school. I first met algebra at the age of 11 in the first year of secondary school. If i remember correctly, a problem like that was typical of what was learned in the first year.

I remember that we were taught algebra, in a mathematics class, by a quite young teacher who was notionally one of the three chemistry teachers. Yet as a graduate with a BSc in Chemistry, teaching mathematics at that and quite possibly much higher levels would have been well within his capabilities.

I remember how he started teaching algebra.

He said something like, "Think of a number, let's have 3, double it and then subtract 1, giving 5.

Then he gradually went on to having an unknown number to start and said that if we double it and subtract 1, suppose we got 9, what was the number with which we started?

Then he introduced the concept of representing the number with which one started as x, and thus explained the idea of having an equation in x and how to solve it.

So, in fact, at the age of 10 I would not have been able to solve that problem using an equation involving x as at that age it was preparing to the the 11+ examination, for which I think that the most advanced part of what I possibly did not know at the time was called mathematics, possibly just known as arithmetic, was long division.

I know we had to do what were called Reading for Meaning exercises where there was text and then questions to be answered where some of them required deducing things, so it is quite possible that a problem like the problem in the web article was encountered, but not presented as arithmetic. But mostly we had the class teacher for most topics, so although arithmetic, spelling, composition were done in separate chunks, it was mostly all in the same room with the same teacher, so pupils not having a timetable for different lessons, the teacher just said that now we are going to do, for example, history.

Alas I have seen it referred to as the culture of "the badge of honour of not being any good at maths" in which some media personalities seem to revel.

It concerns me that that attitude is being presented to young people, because it then can have the effect of people who like maths and are good at maths being ridiculed as being stupid for liking maths. (I know that deeming someone as being stupid because they like maths is illogical - I did not say I think that myself, quite the opposite).

There was all the cultural emphasis on sport.

On that sort of topic I remember an episode of The West Wing where CJ went back to her home town for a 25 years since finishing high school party and lots of people there were very successful, in particular CJ herself. One man worked at an ordinary sort of job, he had not been to college and not had a graduate career. If I remember correctly CJ did not recognise him as (in the fictional backstory) he had become almost bald. He had been the star quarterback in the school football team back then. "I peaked at 17" he said somewhat mournfully.

William