Math Is Fun Forum
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#1 2014-03-09 03:10:43
Counting out his money....
A man is employed to count $10710. He counts at the rate of $180 per minute for half an hour. After this, he counts at the rate of $3 less every minute than the preceeding minute. Find the time taken by him to count the total amount.
Also, explain me how you did this
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#2 2014-03-09 03:20:14
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
Re: Counting out his money....
We have to count how many terms are in that arithmetic progression first.
Let S(A) be sum of the progression
10710=5400+S(A)
S(A)=5310
First term is is 177
Common Difference is -3
Let number of terms be n
10620=n[354+(n-1)*(-3)]
Therefore, n = 59
Total time taken by him to count the total amount is 30+59 which is 89 minutes.
Last edited by ShivamS (2014-03-09 04:22:32)
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#3 2014-03-09 03:24:46
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
Or a recurrence relation.
Total time 30 + 59 = 89
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#4 2014-03-09 03:26:45
Re: Counting out his money....
Thanks 
I was doing a silly error with this one, again...
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#5 2014-03-09 03:40:04
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
Or curve fitting as we discussed in the other thread.
which describes the behavior of the function after the first half hour.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#6 2014-03-09 04:12:24
Re: Counting out his money....
How do you solve the recurrence without doing the algebra Shivam did?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#7 2014-03-09 04:16:17
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
There are a couple of ways to solve a recurrence. One is by curve fitting which is a universal approach to many problems. EVW used it on your problem in the other thread. Another is by iterating the recurrence.You can also use the method of the characteristic polynomial or by generating functions. Of course, M can do everything you will ever need to do on recurrences.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#8 2014-03-09 04:17:29
Re: Counting out his money....
I like Shivam's method better. It's fast.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#9 2014-03-09 04:18:53
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
For the way you approach math I would suggest that you learn many methods.
How do you solve the recurrence
That is the great thing about them, you do not have to solve for them. Like a GF you sometimes leave them in their native state. This is because they are so easy to compute with.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2014-03-09 04:26:31
Re: Counting out his money....
Anything that can be done by recursion can be done by someway better.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#11 2014-03-09 04:29:27
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
In programming they say that the use of recursive calls is not the best way to do anything.
This is a lot more than that.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#12 2014-03-09 04:29:41
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
Re: Counting out his money....
For grade school, I guess it's better to use the regular AP algebraic method to solve such questions, especially on an exam. But sooner or later (if you become a math major), you'll learn and use difference equations anyways.
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#13 2014-03-09 04:37:54
Re: Counting out his money....
difference equations?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#14 2014-03-09 04:38:24
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
Same as recurrence equation.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#15 2014-03-09 04:41:28
Re: Counting out his money....
I still don't see...
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#16 2014-03-09 04:45:02
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
Supposing I asked you what the 100000th Tribonacci number is? A Difference equation is easy to form and to iterate to the answer. The math answer is non - existent, it is too large to post. Not everything has a closed simple form. Most things do not.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#17 2014-03-09 04:52:42
Re: Counting out his money....
Yes, that does not mean you will not do a simple problem in a simple way.
Do not use a cannon to kill a mosquito.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#18 2014-03-09 04:55:39
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
No, I do not. I use the methods of EM, they are a general algorithm for homework, olympiad, brilliant, forum...
Hmmm, have you heard of the Teakettle principle?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#19 2014-03-09 04:57:53
Re: Counting out his money....
No, where is it?
Also, why did you give me the false idea that confucious wrote that?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#20 2014-03-09 05:01:42
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
The quote is attributed to Confucius.
http://www.quoteworld.org/quotes/3150
Bob makes a good point and I do not always check up on quotes.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#21 2014-03-09 05:05:07
Re: Counting out his money....
Please link me to the teakettles.
Will you write a quote book?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#22 2014-03-09 05:18:58
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Counting out his money....
All my quotes were written by someone else. I just get them wrong. Let them write the books.
Start at the top:
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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