What times what equals 100 and adds up to 49?

Answer 1

149

Answer 2

Let the two numbers be a and b. Then ab = 100 and thus b = 100/a, and a + b = 49.

Substituting for b in the second identity gives : a + 100/a = 49

Multiplying throughout by a produces : a2 + 100 = 49a

Re-arranging into standard quadratic form this becomes : a2 - 49a + 100 = 0.

This can be solved using the quadratic formula or by completing the square.

Let's complete the square.

(a - 24.5)2 - 500.25 = 0

(a - 24.5)2 = 500.25

a - 24.5 = √500.25 ≈ ± 22.366

a = 24.5 ± 22.366

Then a = 46.866 and 2.134.............which gives the two numbers required to solve this problem.