SOLUTION: The sum of a number and three times another number is 30. Their product is a maximum. Determine the two numbers

Question 1200643: The sum of a number and three times another number is 30. Their product is a maximum. Determine the two numbers

Answer by ikleyn(52779) (Show Source): You can put this solution on YOUR website!
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The sum of a number and three times another number is 30. Their product is a maximum.
Determine the two numbers
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Let "another" number be x.

Then "the number" is 30-3x.


The product of the two numbers is  x*(30-3x) = 3x*(10-x).


It is a quadratic function, represented by a parabola opened downward. Its roots (the x-intercepts) are 0 and 10.

The maximum is reached at the mid-point between the roots.

This mid-point is x= 5.


Thus "another" number is 5 and "the number" is 30-3*5 = 15.


ANSWER.  The number is 15.  Another number is 5.

Solved, with complete explanations.

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