The sum of two numbers is 31. The product of the two numbers is 150. What are the numbers?

Question

4th grade math question.

Answer 1

Let the two numbers be x and y. So:

x + y = 31

xy = 150

x and y are roots of the equation: z^2 - 31z + 150 = 0

z = [ 31 +/- sqrt(31^2 - 600) ] / 2 = [31 +/- 19]/2 = 25/6

Therefore, x = 25 and y  = 6

Answer 2

let the two numbers be x and y.

Then x + y = 31   ------- (1)

And xy = 150   ---------- (2)

From (1), x = 31 - y

Substitute this expression for x into (2),

(31 - y)y = 150

31y - y^2 = 150

y^2 - 31y + 150 = 0

(y - 6)(y - 25) = 0

Therefore y = 6, y = 25

And x = 31 - 6, x = 31 - 25

i.e. x = 25, y = 6

In other words, the two numbers are just 6 and 25