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August 10th, 2017, 12:55 PM   #1
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Help me please

I have a question:

I have £1,000.

I want to buy as many Magic stones as possible.

Magic stones are £10.

However each time you buy a Magic stone it's price increases by £4.

£10,£14,£18...

How many Magic stones could I buy?

Please show how you work this out.
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August 10th, 2017, 01:26 PM   #2
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Cost of n stones = 10n+4(n(n-1)/2). Set=1000 to find n, and take integer part of answer.
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August 10th, 2017, 03:47 PM   #3
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August 10th, 2017, 09:29 PM   #4
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Type 10 + 14 + 18 + 22 + ... into Google until the running total would exceed 1000.
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August 10th, 2017, 10:55 PM   #5
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If you could buy 'n' magic stones

$\displaystyle 10 + 14 + 18 + 22 .........n\hspace {2mm}times$
$\displaystyle (10+4×0) + (10+4×1)+ (10+4×2) + (10+4×3)... ....... n\hspace {2mm}times $
$\displaystyle [ 10+ 10+10+ 10+ .......... n\hspace{2mm} times] +[4×0+4×1+4×2+4×3 .......... n\hspace{2mm} times] $
$\displaystyle 10n +4 [0+1+2+3+........... n\hspace{2mm}times] $
$\displaystyle 10n +4 \frac {(n-1)×n}{2}$

Equate this with 1000 and round-down the answer
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