Among all pairs of numbers with a sum of 59, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Question

Algebra Word problem 

 

Answer 1

assuming you mean whole numbers...

the maximum area of a rectangle occurs when the rectangle is a square

using the same reasoning, the maximum value occurs when the two numbers are equal but 59 is an odd number so use the numbers 29 and 30 (59/2=29.5, 29.5-0.5=29 and 29.5+0.5=30)

29*30=870

1*58=58

2*57=114

3*56=168

4*55=220

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27*32=864

28*31=868

29*30=870

30*29=870

31*28=868

and the numbers just keep repeating in reverse order