What two numbers are the product of 900 but there sum equal 64?

Answer 1

ANSWER: The two numbers required are not whole numbers. These are 43.135 and 20.865.

Solution 1:

Assuming you want whole numbers:

Prime factorization for 900 is

2 x 2 x 3 x 3 x 5 x 5

You cannot combine these in any way to have a sum that is 64. You can with 65, but not 64.

Solution 2:

Let:

x = first number

y = second number

x * y = 900 (Equation 1)

x + y = 64

x = 64 - y (Equation 2)

Substitute Eq. (2) in Eq. (1):

x * y = 900

(64 - y) y = 900

64y - y2 = 900

- y2 +64y - 900 = 0 (Equation 3)

multiply Eq. (3) by -1

y2 - 64y + 900 = 0

using quadratic equation:

y1 = 43.135 y2 = 20.865

Therefore, the two numbers are 43.135 and 20.865