• 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
8. 8
8
• Level: GCSE
• Subject: Maths
• Word count: 2600

# Mathematics Coursework : The Phone Box Problem

Extracts from this document...

Introduction

## Mathematics Coursework : The Phone Box Problem

Introduction: A woman only has 10 and 20 pence coins to use in a phone box. I have to investigate the number of different ways she could use 10 and 20 pence coins in a phone box. I am also investigating a man who only has 10 and 50 pence coins. I will start off with the woman.
10 pence call
10=10p =1 way
20 pence call
20=10p+10p
20=20p =2 ways
30 pence call
30=10p+10p+10p
30=20p+10p =3 ways
30=10p+20p
40 pence call
40=10p+10p+10p+10p
40=20p+10p+10p
40=10p+20p+10p =5 ways
40=10p+10p+20p
40=20p+20p
50 pence call
50=10p+10p+10p+10p+10p
50=20p+10p+10p+10p
50=10p+20p+10p+10p
50=10p+10p+20p+10p =8ways
50=10p+10p+10p+20p
50=20p+20p+10p
50=20p+10p+20p
50=10p+20p+20p

Pascal´s triangle theory
This should help me to work out long and write out long equations like the ones I am doing

E.g. 50 5 10p =1
1 20p and 3 10p=4 =8 ways
2 20p and 1 10p=3

To get this I used the calculator button which has a big c you put the total number of units at the top then you put the number of 20 pence coins at the bottom. You use the biggest one at the bottom I use 20 pence because it is relevant.

Middle

Investigation 2
In this investigation I am investigating a man who only has 10 and 50 pence coins to use in a phone box. I am going to use Pascal´s triangle to help me in this investigation as well.

10 pence call
10=1 10p=
This would equal 1 different combinations

20 pence call
20=2 10p=
This would equal 1 different combinations

30 pence call
30=3 10p=
This would equal 1 different combinations

40 pence call
40=4 10p=
This would equal 1 different combinations

Results
From these results so far it looks like they are going up by the number 1 so I predict that for a 50 pence call there should be 1 combination. I will now test out this theory by working out how many combinations there are for a 50 pence call.
50 pence call
50=5 10p=1
50=1 50p=1
This would equal 2 different combinations
This is wrong from my prediction so my prediction is wrong. I will now test 60-90 pence calls then look for any pattern.
60 pence call
60=6 10p=1
60=1 50p and 1 10p=2
This would equal 3 different combinations

70 pence call
70=7 10p=1
70=1 50p and 2 10p=3
This would equal 4 different combinations
80 pence call
80=8 10p=1
80=1 50p and 3 10p=4
This would equal 5 different combinations

80 pence call
80=8 10p=1
80=1 50p and 3 10p=4
This would equal 5 different combinations
90 pence call
90=9 10p=1
90=1 50p and 4 10p=5
This would equal 6 different combinations
Results

Conclusion

80p=20p+30p+30p =1
There are 4 different combinations
90 pence call
90p=30p+30p+30p =1
90p=30p+20p+20p+20p =1
90p=20p+30p+20p+20p =1
90p=20p+20p+30p+20p =1
90p=20p+20p+20p+30p =1
There are 4 different combinations
Results
From these if you look my theory only comes in after the 5 term (the 50 pence call). If my theory is correct a 100 pence call should have 7 different combinations.

I will now test my theory for how many combinations there are in a 100 pence call
100 pence call
100p=20p+20p+20p+20p+20p =1
100p=30p+30p+20p+20p =1
100p=20p+30p+20p+30p =1
100p=30p+20p+30p+20p =1
100p=20p+20p+30p+30p =1
100p=30p+20p+20p+30p =1
100p+20p+30p+30p+20p =1
There are 7 different combinations

My prediction was right and there were 7 different combinations for a 100 pence call so my formula is right for two variables:
Tn=(Tn-V1/10)+(Tn-V2/10)
Tn= term number
V= variable
/= Divide
I think that I can adapt my how far you have to go forward until you use the formula I think it would be:
Formula 4
H=V1/10+V2/10
H= how far you have to go back until you can use a formula
V= variable
/= Divide
E.g. 20 and 30 pence
H=V1/10+V2/10
H=20/10+30/10
H=2+3
H=5
Conclusion
If you use formula 3 and formula 4 together you can work out how far forward you can use your formula and what is the next term.

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 ...

An early coin of the period of Nero depicts only his head and little on the back, only showing brief pieces of information about him. One of the coins that I have found shows just this, where only his head and the initials of S C with a wreath around are shown.

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

Investigate the number of different ways he has of entering the 10p and 50p coins into the telephone. Table Amount of money Ways to put it in (in order) No of ways (in order) 20p 10p + 10p 1 40p 10p + 10p + 10p + 10p 1 60p

1. ## Mystery investigation

I walk in & find everyone already there. As usual I am greeted with a frown and a glance at their watch, indicating displeasure. I smile politely & take my seat. All my rookies smile at the prospect of my being put down but I rarely do.

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

The men who sailed in the thirty-oared ship discovered the Persians encamped there more easily, because the sea in this part takes the form of a bay. They therefore brought back word to Alexander that Darius was at hand. Alexander then called together the generals, the commanders of cavalry, and

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

the pay phone are found by adding the previous term together with the third previous term, the result of Tx can be solved by this formula; Tx = T(x-1)+T(x-3) Prediction & Explanation So for 70p, we know it is the equivalent of T7.

2. ## Algebra Coursework (payphone problem).

Let us put this into the formula, to find the "number of ways". Tx = T(x-1)+T(x-3) T7 = T(7-1)+T(7-3) T7 = T6+T4 T7 = 6+3 T7 = 9 Testing The prediction will be tested as to see whether it will work out.

1. ## Small rodents make wonderful pets.

it does...if the pet owner's idea of giving thanks involves squeals and messes. Guinea pigs naturally are not active creatures. While guinea pig experts will say that these creatures only sit still when they are bored, anyone who has owned a guinea pig will disaggree.

2. ## Parachute Investigation.

The height of each test will be measured in metres and centimetres and the average speed of each test will be calculated by the following equation:- Average speed = Distance Time taken The apparatus we will require during the experiment will be listed as the following :- * 40cm �

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