Post a New Question

math

posted by on .

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 - ,

    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

Answer This Question

First Name:
School Subject:
Answer:

Related Questions

More Related Questions

Post a New Question