math

posted by .

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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Working with simple addition and multiplication of positive and negative numbers. Have completed 59 of 60 problems on a worksheet, I am stumped by one of them. For example Two numbers are given 30 and 13, You must find two number multiplied …
  2. Math

    these numbers in ordered pairs are related to each other. 1.(1,2), (3,4), (5,6), (0,__), (10,11), (2,___), (___,7), (8,__) 2. (9,3), (3,1), (12,__), (__,2), (___,7), (8,___) 3. (4,9), (5,11), (2,5), (6,__), (__,7), (10,__), (__,3) …
  3. math

    hese numbers in ordered pairs are related to each other. 1.(1,2), (3,4), (5,6), (0,__), (10,11), (2,___), (___,7), (8,__) 2. (9,3), (3,1), (12,__), (__,2), (___,7), (8,___) 3. (4,9), (5,11), (2,5), (6,__), (__,7), (10,__), (__,3) 4. …
  4. Math

    these numbers in ordered pairs are related to each other. 1.(1,2), (3,4), (5,6), (0,__), (10,11), (2,___), (___,7), (8,__) 2. (9,3), (3,1), (12,__), (__,2), (___,7), (8,___) 3. (4,9), (5,11), (2,5), (6,__), (__,7), (10,__), (__,3) …
  5. Math

    List the common multiples from 1 to 100 for each pair of numbers. Then find the least common multiple for each pair. 8 and 12, 3 and 15, 7 and 11, 9 and 10, 24 and 36, 20 and 25, 42 and 14, 30 and 12 Then find pairs of numbers for …
  6. Math

    1. What two numbers can be multiplied to equal -60 and added to be -11?
  7. math

    Find all pairs (m,n) of positive integers such that m(n+1) + n(m-1) = 2000
  8. math

    A. Find 3 pairs of numbers for which the least common multiple equals the product of the the 2 numbers. B. Look at the pairs of numbers you found in part a. What is true about all 3 pairs of numbers?
  9. Math

    Find three pairs of numbers for which the LCM (least common multiple) is the product of the two numbers; The pairs and LCMs are: 8 and 12: 24; 3 and 15: 15; 7 and 11: 77; 9 and 10: 90; 24 and 36: 72; 20 and 25: 100; 14 and 42: 42; …
  10. Math

    Find all pairs of integers such that when they are added they equal 100, and when they are multiplied they are at least 2000.

More Similar Questions