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Introduction
A pay phone will take only 10p, 20p, 50p, and £1 coins. ... She can put the coins into the pay phone in any order. ... The woman is going to make a phone call costing any multiple of 10p. ...
A man also wants to use the pay phone. ... The woman is going to make a phone call costing any multiple of 10p. Investigate the number of different ways she could put the 10p and 20p coins into the pay phone. ...
Prediction
Looking at the table above, we know that;
30p = T3 = T2+T1
40p = T4 = T3 +T2
50p = T5 = T4+T3
So, 60p´s prediction will be
60p = T6 = T5+T4
Explanation
As every "total no of combinations" of putting the coins into the pay phone are found by adding the 2 previous terms, the result of Tx can be solved by this formula;
Tx = T(x-1)+T(x-2)
Prediction & Explanation
So, for 60p we know it is the equivalent of T6. ... Starting of with 10p and 30p, I will investigate the number of different ways you could put the 10p and 30p coins into the pay phone. The phone call will cost any multiple of 10p.
Multiple of 10p Combinations for 10, 30p Total no of combinations Algebra/Terms
10p 10 1 T1
20p 10,10 1 T2
30p 10,10,10,30 2 T3
40p 10,10,10,1010,3030,10 3 T4 = T3+T1
50p 10,10,10,10,1010,10,3030,10,1010,30,10 4 T5 = T4+T2
60p 10,10,10,10,10,1030,3010,10,10,3030,10,10,1010,30,10,1010,10,30,10 6 T6 = T5+T3
Prediction
Looking at the table at the table above, we know that;
40p = T4 = T3+T1
50p = T5 = T4+T2
60p = T6 = T5 +T3
So, 70p´s prediction will be
70p = T7 =T6+T4
Explanation
As every "total no of combinations" of putting the coins into 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. ... The number of different ways you could put the two coins into the pay phone is shown in the table on the next page. The phone call will cost any multiple of 10p.
Multiple of 10p Combinations for 10p,40p Total no of combinations Algebra/Terms
10p 10 1 T1
20p 10,10 1 T2
30p 10,10,10 1 T3
40p 10,10,10,1040 2 T4
50p 10,10,10,10,1010,4040,10 3 T5 = T4+T1
60p 10,10,10,10,10,1010,10,4040,10,1010,40,10 4 T6 = T5+T2
70p 10,10,10,10,10,10,10,10,10,10,4040,10,10,1010,40,10,1010,10,40,10 5 T7 = T6+T3
80p 10,10,10,10,10,10,10,1040,4010,10,10,10,4040,10,10,10,1010,40,10,10,1010,10,40,10,1010,10,10,40,10 7 T8 = T7+T4
90p 10,10,10,10,10,10,10,10,1010,40,4040,10,4040,40,1010,10,10,10,10,4040,10,10,10,10,1010,40,10,10,10,1010,10,40,10,10,1010,10,10,40,10,1010,10,10,10,40,10 10 T9 = T8+T5
Prediction
Looking at the table above, we know that;
50p = T5 = T4+T1
60p = T6 = T5+T2
70p = T7 = T6+T3
80p = T8 = T7+T4
90p = T9 = T8+T5
So, £1´s prediction will be
£1 = T10 = T9+T6
Explanation
As every "total no of combinations" of putting the coins into the pay phone are found by adding the previous term together with the forth previous term, the result of Tx can be solved by this formula;
Tx = T(x-1)+T(x-4)
Prediction & Explanation
So for £1, we know that it is the equivalent of T10.
Approximate Word count = 3019
Approximate Pages = 12.1
(250 words per page double spaced)
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