Lucy T.

asked • 10/09/15

Among all pairs of numbers with a sum of 34, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Among all pairs of numbers with a sum of 34, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

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Arthur D. answered • 10/09/15

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x+y=34
xy=max
x=34-y
y(34-y)=0
34y-y^2=0
use -b/2a
-34/-2=17
17*17=289
16*18=288
15*19=285
14*20=280
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Mark M.

Taking a clue from geometry, the rectangle with the greatest area (maximum product of two numbers) is the square.
The pair of numbers, for 34, is 34/2, or 17.
For 100, it would be 50 · 50.
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10/09/15

Arthur D.

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Good point, Mark.
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10/10/15

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