Fluctuating prices?

Algebra Level 2

If the price of an item was increased by M % M\% , and then it was decreased by N % N\% such that the price remains unchanged, what is the relationship between M M and N N ?

M N = 10000 MN = 10000 ( 100 − M ) ( 100 + N ) = 10000 (100-M)(100+N) = 10000 M + N = 100 M+N= 100 ( 100 + M ) ( 100 − N ) = 10000 (100+M)(100-N) = 10000

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Jesse Nieminen
Aug 14, 2016

Increasing the price by M % M\% and then decreasing it by N % N\% and the price still being the same as in the beginning implies that

( 1 + M 100 ) ( 1 − N 100 ) = 1 ⟹ ( 100 + M ) ( 100 − N ) = 10000 \left(1 + \dfrac M{100}\right)\left(1 - \dfrac N{100}\right) = 1 \implies \boxed{\left(100 + M\right)\left(100 - N\right) = 10000}

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