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Algebra Level 1

a + b + 6 = 97 a + b + 6 = 97

If a a and b b are positive integers satisfying the equation above, what is the maximum value of 100 b 100b ?


The answer is 9000.

I Gede Arya Raditya Parameswara by I Gede Arya Raditya Para… , 17

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1 solution

Ayush G Rai
Nov 4, 2016

For b to be maximum we must first minimize a as much as possible.So the least value a can take is 1 1 since it must be a positive integer.
So, b + 1 + 6 = 97 ⇒ b = 90. b+1+6=97\Rightarrow b=90. Therefore the maximum value of 100 b = 100 × 90 = 9000 . 100b=100\times 90=\boxed{9000}.

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How about Am-Gm?? @Ayush Rai

I Gede Arya Raditya Parameswara - 4 years, 5 months ago

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it won't work.I don't why

Ayush G Rai - 4 years, 5 months ago

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Thank's good work @Ayush Rai

I Gede Arya Raditya Parameswara - 4 years, 5 months ago

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@I Gede Arya Raditya Parameswara – oh..i understood why it doesn't work.Am-Gm works for positive reals but here it is mentioned that a and b should be a positive integer.

Ayush G Rai - 4 years, 5 months ago

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