Homework Help Forum: math

Posted by jake on Monday, August 10, 2009 at 7:22pm.

divide 100 loaves of bread amoung 5 men so that the amounts are in arithmetic progression ( increase by the same amount each time) and the sum of the three largest shares is seven times the sum of the two smallest.

• math - Reiny, Monday, August 10, 2009 at 7:50pm

  use the formula for the general term of an arithmetic sequence the terms would be a, a+d, a+2d, a+3d, and a+4d adding them up: 5a + 10d = 100 or a + 2d = 20 after dividing by 5 given: sum of 3 largest equals seven times the sum of the two smallest, or a+2d + a+3d + a+4d = 7(a + a+d) 3a + 9d = 14a + 7d 2d = 11a from first equation a = 20 - 2d into the second: 2d = 11(20-2d) 2d = 220 - 22d 24d = 220 d = 220/24 = 55/6 subbing back: a = 20 - 2(55/6) = 5/3 checking: first term is 5/3 or 10/6 is 10/6 + 65/6 + 120/6 + 175/6 + 230/6 equal to 100 ? YES!

  
  

• math - Anonymous, Thursday, August 13, 2009 at 7:08pm

  50

  
  

• math - bich, Thursday, August 13, 2009 at 9:08pm

  374811518532311154222000151220025110120126973463765827396654565868436844654656654524547654453646683765476756646754565446544665485658447

  
  

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