You can
put this solution on YOUR website!The cost of producing an initial bicycle is £1200 and each successive bicycle there after cost £50 less than the last one. How many bicycles can be made for £10000?
I believe I know the formula, however because the Sn is 'less than' I cant seem to get to the answer!!
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Series: 1200 + 1150 + 1100 + ...
S(n) < 10,000
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a = 1200 and d = -50
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Solve:
S(n) = (n/2)(a(1) + a(n))
10000 = (n/2)(1200 + a(n))
20000= (n)(1200 + 1200 +(n-1)(-50))
20000 = (n)(2400 -50n+50)
20000 = n(2450 - 50n)
-50n^2 +2450n - 20000 = 0
n^2 - 49n + 400 = 0
n = 38.65 or n = 10.35
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Now consider the inequality:
20000 < n(2450n-50n)
n^2 -49n + 400 < 0
The parabola opens up so the
solutions for the inequality are
between the roots.
10.35 < n < 38.65
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Cheers,
Stan H.
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