Pay phone problem

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                               Jen ball 10 dolbe pay phone problem IntroductionA 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 call10=10p =1 way20 pence call20=10p+10p20=20p =2 ways30 pence call30=10p+10p+10p30=20p+10p =3 ways30=10p+20p40 pence call40=10p+10p+10p+10p40=20p+10p+10p40=10p+20p+10p =5 ways40=10p+10p+20p40=20p+20p50 pence call50=10p+10p+10p+10p+10p50=20p+10p+10p+10p50=10p+20p+10p+10p50=10p+10p+20p+10p =8ways50=10p+10p+10p+20p50=20p+20p+10p50=20p+10p+20p50=10p+20p+20pPascal’s triangle theoryThis should help me to work out long and write out long equations like the ones I am doingE.g. 50 5 10p =11 20p and 3 10p=4 =8 ways2 20p and 1 10p=3To 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. The way that Pascal made up this theory was he got a triangle and started with 1 at the top and started adding them up as he went down like this:11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 7 1He did this for the rest of the way down. Instead of a calculator Pascal would have used the number of units added up to see how far he had to go down and the number of units in the biggest value to see how far he would of gone across.E.g.505 10p =11 20p and 3 10p=4 down and 1 across2 20p and 1 10p=3 down and 2 across You then look at where the numbers would be on the triangle and add them up that would come to 1+4+3 which would equal 8.InvestigationI am now going to use Pascal’s triangle in my investigation to shorten the length of my equations.60 pence call60= 6 10p =160=1 20p and 4 10p=560=2 20p and 2 20p=660=3 20p=1This would equal 13 different combinations70 pence call70=7 10p=170=1 20p and 5 10p=670=2 20p and 3 10p=1070=3 20p and 1 10p=4This would equal 21 different combinations80 pence call80=8 10p=180=1 20p and 6 10p=780=2 20p and 4 10p=1580=3 20p and 2 10p=1080=4 20p=1This would equal 34 different
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combinationsResultsThis is a table of my results and a prediction for this far into this investigationCost of phone call 10 pence 20 pence 30 pence 40 pence 50 pence 60 pence 70 pence 80 pencenumber of combinations 1 2 3 5 8 13 21 34By these results I would say this was the Fibinachi series which means to work out the next one you have to add the two previous terms to work out the next term. You can right it as the equation:Tn=(Tn-1)+(Tn-2)Tn means term numberPredictionI would say using the Fibinachi series the next number for a 90 pence ...

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