What two numbers have a product of 6400 and a sum of 160?

Answer 1

I'll define two variables, x and y.

x = the value of the 1st number

y = the value of the 2nd number

Equation 1:

xy = 6400

Equation 2:

x + y = 160

x + y - y = 160 - y

x = 160 - y

Plug this into the first equation

(160 - y) * y = 6400

Simplify

160y - y2 = 6400

-y2+160y = 6400

-y2 + 160y - 6400 = 6400 - 6400

-y2 + 160y - 6400 = 0

-(y2 - 160y + 6400) = 0

-1*-(y2 - 160y + 6400) = 0 * -1

y2 - 160y + 6400 = 0

(y - 80)2 = 0

y - 80 = √(0)

y - 80 = 0

y - 80 + 80 = 0 + 80

y = 80

Use the original 2nd equation to find x

x + y = 160

x + (80) = 160

x + 80 = 160

x + 80 - 80 = 160 - 80

x = 80

Both numbers are 80.

I hope this made sense to you.