Question 824043
A Nintendo DS costs one hundred and twenty British pounds sterling (£120). I decide today, 17th April 2013, to put 10p aside. Tomorrow I’ll put 15p, the day after 20p, the day after that 25p and
so on, increasing the amount by 5p every day. At which date will I have enough to buy the
Nintendo?
£1 = one pound = 100 pennies = 100p
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Series: 10 + 15 + 20 + 25 + ...
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Arithmetic Series with a = 10 and d = 5
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Formula: S(n) = (n/2)(A + L)
L = A + (n-1)d
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A = 10
d = 5
S(n) >= 120
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120 =< (n/2)(10+L)
240 =< n(10+(A+(n-1)5)
240 =< n(10 + 10+(n-1)5)
240 =< n(20 + 5n-5)
240 =< n(15 + 5n)
48 =< n(3+n)
n^2 + 3n - 48 >= 0
n = >= 6
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Answer:: 17th + 6 = 23rd
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Cheers,
Stan H.