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The Payphone Problem

“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.

Key

Green - 1st block

Purple- 2^nd block       

Blue- 3^rd block

Observation

The sequence starts when another coin is put in (a different coin)

The second block goes up by 2, 3, and 4…

And the third block goes up by 1

I think the next value that is 70p will be 21 ways (in order) I found this out using this formula 'background:yellow; '>OR + NR = next result

When

OR is old result

NR is new result

So now to find 70p will be 'background:yellow; '>8 + 13 = 21

Prediction

I don’t think the graph might give me a reasonable result for a conclusion, but it might help to figure out the next set of results without working it out.

I have decided to draw a graph of the no of ways and amount of money to try and make a conclusion.

Graph

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 n^th term

Second table

Graph

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

It suggests that 70p will have 4 ways not in order

A man also wants to use the pay phone. He has plenty of 10p and 50p coins. He has no other coins. He wishes to make a telephone call costing any multiple of 10p.

Question?

1.    Investigate the number of different ways he has of entering the 10p and 50p coins into the telephone.

Table

Black-First block

Green-second block

Blue-third block

Observation

It stays the same until it reaches 50 then it increases by 2, 3, and 4…

The same also happens with the blue block it stays the same but when it reaches 50 it increases by 2, 3, 4…

Prediction for graph

I will try to find out the next value for the no of ways for £1.20. I predict that would have about 11 ways

Graph

This graph suggests that £1.20 will have 11 ways

Table

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.

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.

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