Readjust sides to Readjust Area
Let and be positive integers less than 100.
If the length of a certain rectangle is increased by , and the width of the same rectangle is decreased by , then the resultant area is increased by .
Find .
The answer is 136.
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1 solution
An increase of 2 0 . 1 7 % means that the total area is now 1 0 0 % + 2 0 . 1 7 % = 1 2 0 . 1 7 % = 1 . 2 0 1 7 of the original rectangle.
12017 is a product of 2 primes , namely 1 2 0 1 7 = 6 1 × 1 9 7 .
As we are told that a and b are both positive integers less than 100, then 1 2 0 1 7 = ( 1 0 0 + a ) ( 1 0 0 − b ) = ( 1 9 7 ) ( 6 1 ) . Thus a = 1 9 7 − 1 0 0 = 9 7 and b = 1 0 0 − 6 1 = 3 9 . The answer is a + b = 9 7 + 3 9 = 1 3 6 .