The sum of two numbers are 60. Find the numbers if their product is a maximum

Question

How come for this question “y=x+60” when using quadratics, and not “x+y=60” since the 2 numbers equal to 60

Answer 1

Let x and y be the two numbers.

x + y = 60

y = 60 - x

xy = x(60-x) = -x² + 60x

This is an inverted parabola, so its vertex is the maximum. The x-coordinate of the vertex is:

x = -b/2a = -60/2(-1) = 30

y = 60 - x = 60 - 30 = 30

x = 30, y = 30