Best Answer

Let one number be x, the other is 83-x

Their product is x(83-x)

so the function is

f(x)=x(83-x)

or f(x)=83x-x2

Q: If the sum of two positive numbers is 83 find a function that models their product P in terms of x one of the numbers?

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If x is one of the numbers and y the other, then their sum is x+y = 53. So y = 53-x where x>0 and y>0 implying that x<53. Then, their product, P = x*y = x*(53-x) = 53*x - x2 for 0<x<53 [P is not defined for other values of x]

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If x is one of the numbers then the other is (89-x). Both these are positive, so x>0 and 89-x>0 or x<89. Then P(x) = x*(89-x) = 89x-x2 where 0<x<89

If x is one of the numbers and y the other, then their sum is x+y = 53. So y = 53-x where x>0 and y>0 implying that x<53. Then, their product, P = x*y = x*(53-x) = 53*x - x2 for 0<x<53 [P is not defined for other values of x]

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