Math Is Fun Forum

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Non - Routine Algebra

Yes, that would do it.

That also works in the event of there being joint winners, who would then be named as such.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

CurlyBracket

Member

From: Your Maths Textbook

Registered: 2022-01-03

Posts: 155

Re: Non - Routine Algebra

Ok, done. Thanks, phrontister.

Here’s the next one.

Question 6

The combined age of a man and his wife is six times the combined ages of their children.

Two years ago their united ages were ten times the combined ages of their children.

Six years hence their united ages will be three times the combined ages of the children.

How many children do they have?

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Filling the unforgiving minute with sixty seconds’ worth of distance run!

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Non - Routine Algebra

Hi CurlyBracket;

Question 6: How many children do they have?

They have 3 children.

Last edited by phrontister (2022-08-30 13:11:08)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

CurlyBracket

Member

From: Your Maths Textbook

Registered: 2022-01-03

Posts: 155

Re: Non - Routine Algebra

Correct answer! And great explanation too.

Easy one now :

Question 7

There are 3 numbers.

The second is greater than the first by the amount the third is greater than the second. 

The product of the two smaller numbers is 85.

The product of the two larger numbers is 115.

If the numbers are x, y, z with x<y<z then the value of (2x + y+ 8z) is?

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Filling the unforgiving minute with sixty seconds’ worth of distance run!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Non - Routine Algebra

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

CurlyBracket

Member

From: Your Maths Textbook

Registered: 2022-01-03

Posts: 155

Re: Non - Routine Algebra

Hello! I'm back...for now. I'm going to try and stick around for a bit more.

Correct answer, Bob! Woop woop

Question 8

The following diagrams show the first four steps in forming the Sierpiński triangle.

Diagram because I've forgotten how images work

Step 1: Start with an equilateral triangle of side length 1 unit.
Step 2: Subdivide it into four smaller congruent equilateral triangles and colour the
central one blue.
Step 3: Repeat Step 2 with each of the smaller white triangles.
Step 4: Repeat again.

The question has 3 parts (fancy, fancy):

a. How many white triangles after n steps?
b. Side length of a white triangle at Step n?
c. Fraction of the area that is still white at Step n?

Have fun

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Filling the unforgiving minute with sixty seconds’ worth of distance run!

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Non - Routine Algebra

Hi CurlyBracket;

I got the following answers from observing sequence results:

I think they work for all n values!

Last edited by phrontister (2024-11-16 04:05:37)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Non - Routine Algebra

hi Phro,

I agree with your answers to a and c but not b.

When we start I'll take it that n = 0; we have a single white triangle side =1

At step 1 the white triangles have side = 1/2 = 1/(2^1)

At step 2 the white triangles have side = 1/4 = 1/(2^2)

.....................

If you spot a sequence and use it to get algebraic answers that seems ok to me. But all that's missing is to prove that the sequences are valid.  You can do that by, for instance, in each step the previous number of whites is made into four new smaller triangles, one of which is blue so 3/4 are still white. So each step increases the number of whites by a multiplier of times 3/4

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Non - Routine Algebra

Hi Bob;

When we start I'll take it that n = 0; we have a single white triangle side =1

Step 1: Start with an equilateral triangle of side length 1 unit.

To me that means for Step 1, n = 1 (and for Step 2, n = 2; Step 3, n = 3; ...etc).

Looks like I got the Part c formula wrong in post #32, so here's my revised set of answers:

I drew it all up in Excel (see image), and it shows that the revised set works (I think!)

Btw, I'd expected to find the above equilateral triangle area formula on MIF, here - Area of Triangles - but it's not there.

Last edited by phrontister (2024-11-16 23:54:04)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Non - Routine Algebra

Ok so I didn't read the question.

So now I'm getting

3^(n-1)       (1/2)^(n-1)       (3/4)^(n-1)

When n=1 don't we want just one white triangle?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Non - Routine Algebra

When n=1 don't we want just one white triangle?Bob

Oops! Must've been my turn to bumble!!

Of course n=1 has only 1 white triangle!

New Excel image below, updated to 100% accuracy!!

Last edited by phrontister (2024-11-18 19:20:23)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson