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PAYPHONE. The woman is going to make a phone call costing any multiple of 10p. Investigate the number of different ways she could put 10p and 20p coins into the payphone.

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Introduction

The Payphone Problem Maths Coursework

“I will be investigating a pay phone problem in which I will be using some information and my knowledge to guide me. I will have to make predictions and conclusion’s and use tables to show my work.”

A pay phone will take only 10p, 20p, 50p and £1 coins.

A woman has plenty of 10p and 20p coins. She has no other coins. She can put the coins into the pay phone in any other.

Question?

  1. The woman is going to make a phone call costing any multiple of 10p. Investigate the number of different ways she could put 10p and 20p coins into the payphone.

Prediction

I predict that my table will have a relationship and show me how to find a sequence or the nth term.

Table.

Amount of money

Ways of putting it in (in order)/

No of ways to put it in (in order)

10p

10p

1   

20p

10p + 10p

20p

2       1+1

30p

10p + 10p + 10p

20p + 10p

10p + 20p;

3       1+2

40p

10p + 10p + 10p + 10p

20p + 20p

20p + 10p + 10p

10p + 20p + 10p

10p + 10p + 20p

5       1+1+3

50p

10p + 10p + 10p + 10p + 10p

20p + 20p + 10p

10p + 20p + 20p

20p + 10p + 20p

20p + 10p + 10p + 10p

10p + 20p + 10p + 10p

10p + 10p + 20p + 10p

10p + 10p + 10p + 20p

8       1+3+4

60p

10p + 10p + 10p + 10p + 10p + 10p

20p + 20p + 20p

20p + 20p + 10p + 10p

10p + 20p + 20p + 10p

10p + 10p + 20p + 20p

20p + 10p + 10p + 20p

10p + 20p + 10p + 20p

20p + 10p + 20p +10p

20p + 10p + 10p + 10p + 10p

10p + 20p + 10p + 10p + 10p

10p + 10p + 20p + 10p + 10p

10p + 10p + 10p + 20p + 10p

10p + 10p + 10p + 10p + 20p

13       1+1+6+5

...read more.

Middle

This graph suggests that the next result is 21, which is correct because it’s the right answer in my formula.

Conclusion

I have observed that the amount of money may be directly proportional to number of ways2.

The result isn’t good for the graph because they hardly seam to have a relation ship apart from the blocks.

Prediction

I predict that the second table will be more reasonable than the first in terms of it will be easier to tell the nth term

Second table

How much is put in

How much is put in (not in order)

How many ways (not in order)

10p

10p

1

20p

10p + 10p

20p

2     1+1

30p

10p + 10p + 10p

20p + 10p

2     1+1

40p

10p + 10p + 10p + 10p

20p + 20p

10p + 10p + 20p

3     1+1+1

50p

10p + 10p + 10p + 10p + 10p

20p + 20p + 10p

20p + 10p + 10p + 10p

3     1+1+1

60p

10p + 10p + 10p + 10p + 10p + 10p

20p + 20p + 20p

20p + 20p + 10p +10p

20p + 10p + 10p + 10p + 10p

4     1+1+1+1

Graph

image01.jpg

In this graph the graph the amount of ways goes in steps i.e. 2,2 3,3 4,4 etc

...read more.

Conclusion

50p + 50p

50p + 10p +10p + 10p + 10p + 10p

3         1 + 1 + 1

Observation

Just like the former table that was not in order this one goes in steps after the next coin is put in.

Prediction

I think the next graph will go in steps so the next value will be 3 ways.

image03.png


Graph 

Observation

I observed that this graph also goes in steps so the next value according to my graph will be 3 not in order.

Conclusion

In a payphone the sequence starts or the no of blocks as I have illustrated above increases when a new coin is added

In all the amounts that will be put in the payphone in the multiple of 10 the sequence will only start when a different coin is put in.

Using a 20p and a 10p coin to find the next formula you will have to add the now result and old result, using a 10p and 50p coin finding the next result using a formula isn’t possible.

If you’re using a 10p and a 20p coin and you’re using it not in order then it will go 1 22 33 44 55 66 and so on.

...read more.

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