At a local village gala, the entire population turned up, 500 people. The event raised £3,000. Tickets were priced as follows:
£7.48 men
£7.12 women
£0.45 children.
How many men,women and children were there?

• m + w + c = 500
  m = 500 - w - c
  748m + 712w + 45c = 300 000
  
  Now
  
  748 (500 - w - c) + 712w + 45c = 300 000
  374 000 - 748w - 748c + 712w + 45c = 300 000
  74 000 = 36w + 703c
  
  solving this for integer values of m,w,c
  we get
  
  m= 149, w = 259, c= 92
• 12 years agoHelpfull: Yes(4) No(1)
• Women = 259
  Men = 149
  Children = 92
  
  Women = 259 *7.12 = 1844.08
  Men = 149 *7.48 = 1114.52
  Children = 92 *0.45 = 41.4
  
  Total :
  Men + Women + Children = 149 + 259 + 92 = 500 peoples.
  1844.08 + 1114.52 + 41.4 = 3000
• 12 years agoHelpfull: Yes(3) No(3)
• Women = 259
  Men = 149
  Children = 92
  
  Women = 259 *$7.12 = $1844.08
  Men = 149 *$7.48 = $1114.52
  Children = 92 *$0.45 = $41.4
  
  Total :
  Men + Women + Children = 149 + 259 + 92 = 500 peoples.
  $1844.08 + $1114.52 + $41.4 = $3000
• 12 years agoHelpfull: Yes(2) No(3)
• @ Vignesh,
  
  How did you get these values ?
• 12 years agoHelpfull: Yes(2) No(0)
• w is women
  c is children
  (500-w-c) 7.48 + 7.12 w + 0.45 c = 3000
  so we get 0.36w + 7.03 c = 740
  multipy by 100
  36w + 703 c = 74000
  Then : if men were the only one it will make 500 x 7.48 = 3740 so 740 too much
  if women were the only one it will make 500 x 7.12 = 3560 so 560 too much
  So, we may considere that the maximum children is 740/7.48-0.45 = 105
  And the less children possible is 560/7.12-045 = 84
  Let take the median between 105 and 84 = 95
  Now check around 95 children to find the only integer possible :
  Nb of women for 95 children = (74000-703 x 95) / 36 = 200,4167 women not OK
  Nb of women for 94 children = (74000-703 x 94) / 36 = 219,9444 women not OK
  Nb of women for 96 children = (74000-703 x 96) / 36 = 180,8889 women not OK
  Nb of women for 93 children = (74000-703 x 93) / 36 = 239,4720 women not OK
  Nb of women for 97 children = (74000-703 x 97) / 36 = 161,3611 women not OK
  Nb of women for 92 children = (74000-703 x 92) / 36 = 259 women THIS IS OK
  Why divide by 36 ? because each time we increase the nb of women the total is +36
  So, in a very few operations we find 92 children, 259 women and 500-259-92 = 149 men
• 4 years agoHelpfull: Yes(1) No(0)