Question

In the answer space below, provide the larger of the two positive integers that add up to 60 and have the largest possible product.

Answer 1

Answer:

The two positive integers are 30 and 30

Step-by-step explanation:

Let

x------> the larger  positive integer

y-----> the smaller positive integer

P----> the product o the two positive integers

we know that

$x+y=60$

$y=60-x$ -----> equation A

$P=xy$ ----> equation B

substitute equation A in equation B

$P=x(60-x)$

$P=60x-x^{2}$

This is the equation of a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the largest possible product

Using a graphing tool

The vertex is the point (30,900)

That means------> For $x=30$ The largest possible product is $900$

and

$y=60-x$ ------> $y=60-30=30$

therefore

The two positive integers are 30 and 30