The product of two whole numbers is 180 and their sum is36. What are the two numbers?

6,30

Step-by-step explanation:

The product of two whole numbers is 180

xy = 180

and their sum is 36

x+y = 36

x = 36-y

Substitute this into the first equation

(36-y) (y) = 180

36y - y^2 = 180

Add y^2 to each side

36y = 180 + y^2

Subtract 36y from each side

0 = y^2 - 36y + 180

Factor

0 = (y-6) (y-30)

Using the zero product property

y-6 = 0 y-30 = 0

y = 6 y = 30

Now we need to find x

If y = 6

x = 36-6=30

If y = 30

x = 36-30=6

The two numbers are 30 and 6