Posted by **Omar** on Wednesday, February 13, 2013 at 2:15pm.

Find all pairs of numbers such that when they are added they equal 100, and when

they are multiplied they are at least 2000.

- math -
**Steve**, Wednesday, February 13, 2013 at 3:08pm
maximum product occurs when a=b=50

That makes the product 2500

The larger a gets, the smaller b must get, so try

a=40 b=60: ab=2400

a=30 b=70: ab=2100

a=20 b=80: ab=1600

and narrow in on it.

Or, algebraically,

a(100-a) >= 2000

a^2 - 100a + 2000 <= 0

10(5-√5) <= a <= 10(5+√5)

27.6 <= a <= 72.3

so, 28 < a <= 72

check:

28*72 = 2016

27*73 = 1971

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