• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
• Level: GCSE
• Subject: Maths
• Word count: 1183

# 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.

Extracts from this document...

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 + 10p20p 2       1+1 30p 10p + 10p + 10p20p + 10p10p + 20p; 3       1+2 40p 10p + 10p + 10p + 10p20p + 20p20p + 10p + 10p10p + 20p + 10p10p + 10p + 20p 5       1+1+3 50p 10p + 10p + 10p + 10p + 10p20p + 20p + 10p10p + 20p + 20p20p + 10p + 20p20p + 10p + 10p + 10p10p + 20p + 10p + 10p10p + 10p + 20p + 10p10p + 10p + 10p + 20p 8       1+3+4 60p 10p + 10p + 10p + 10p + 10p + 10p20p + 20p + 20p20p + 20p + 10p + 10p10p + 20p + 20p + 10p10p + 10p + 20p + 20p20p + 10p + 10p + 20p10p + 20p + 10p + 20p20p + 10p + 20p +10p20p + 10p + 10p + 10p + 10p10p + 20p + 10p + 10p + 10p10p + 10p + 20p + 10p + 10p10p + 10p + 10p + 20p + 10p10p + 10p + 10p + 10p + 20p 13       1+1+6+5

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 + 10p20p 2     1+1 30p 10p + 10p + 10p20p + 10p 2     1+1 40p 10p + 10p + 10p + 10p20p + 20p10p + 10p + 20p 3     1+1+1 50p 10p + 10p + 10p + 10p + 10p20p + 20p + 10p20p + 10p + 10p + 10p 3     1+1+1 60p 10p + 10p + 10p + 10p + 10p + 10p20p + 20p + 20p20p + 20p + 10p +10p20p + 10p + 10p + 10p + 10p 4     1+1+1+1

Graph

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

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.

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.

This student written piece of work is one of many that can be found in our GCSE Pay Phone Problem section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Pay Phone Problem essays

1. ## Were coins used in the Roman Empire more for propaganda purposes or as a ...

The reverse side of these coins where this information was portrayed can be backed up by literary texts, one by Suetonius and the other Tacitus. The depiction of Poppea on Nero's coin shows that Nero wanted to announce to his people that he had married this woman.

2. ## Arrian, The Anabasis of Alexander, together with the Indica, E

For the Macedonian phalanx had been broken and had disjoined towards the right wing, because Alexander had dashed into the river with eagerness, and engaging in a hand-to-hand conflict was already driving back the Persians posted there; but the Macedonians in the centre had not prosecuted their task with equal

1. ## Origins of Money and of Banking

secondary or derived function in one place may have been in some other region the original which gave rise to a related secondary function... The logical listing of functions in the table therefore implies no priority in either time or importance, for those which may be both first and foremost reflect only their particular time and place."

2. ## The woman is going to make a phone call costing any multiple of 10p. ...

Prediction & Explanation So, for 60p we know it is the equivalent of T6. Let us put this into the formula, to find the "number of ways". Tx = T(x-1)+T(x-2) T6 = T(6-1)+T(6-2) T6 = T5+T4 T6 = 8+5 T6 = 13 Testing The prediction will be tested as to see whether it will work out.

1. ## Algebra Coursework (payphone problem).

Multiple of 10p Combinations for 10p, 20p Total no of combinations Algebra/Terms 60p 10,10,10,10,10,1020,20,2010,10,10,10,2020,10,10,10,1010,20,10,10,1010,10,20,10,1010,10,10,20,1010,10,20,2020,10,10,2020,20,10,1010,20,20,1010,20,10,2020,10,2010, 13 T6 = T5+T4 The pattern of the different number of ways a multiple of 10p can be used, using 10p and 20p coins only, is recorded below; 10p- 1 20p- 2 30p- 3 40p- 5

2. ## Small rodents make wonderful pets.

Imagine that your beloved block of wood was once part of a hardy, eighty-foot-tall tree, who had majestically grown from a tiny acorn in the dense forrests of Canada! Who would want to be introducing a new pet to their friends and say "This is Bob and he came from the pet store and well...uhh...that's about it, actually"?

1. ## The Undetermined Amount.

Johnson is having a hard time motivating his self to push through the crowds and clock in. Johnson is feeling apprehensive about seeing his boss and puts his head down hoping to avoid confrontation. She calls out his name and he can see the anger in her face.

2. ## The payphone Problem

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 Key Green - 1st block Purple- 2nd block Blue- 3rd block

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to