Jack and Danny are bricklayers. Jack can build a certain brick wall in 8 hours whereas Danny takes 11 hours. If they work together, their combined rate decreases by 7 bricks an hour, and it only takes them 5 hours to build the wall together. Find the number of bricks in the wall

• let the number of brick in the wall be x
  
  jack can lay x bricks in 8 hrs => x/8 bricks per hour
  danny can lay x bricks in 11 hrs => x/11 bricks per hour
  
  combined rate = x/8 + x/11 bricks per hour
  
  working together causes their combined rate to decrease by 7 bricks per hour
  
  combined rate while working together = x/8 + x/11 - 7 bricks per hour
  
  it takes them 5 hours to build the wall
  
  5*(x/8 + x/11 - 7) = x
  
  expand the brackets
  
  5x/8 + 5x/11 - 35 = x
  
  now solve it by multiply both sides by 88
  
  55x + 40x - 3080 = 88x
  
  95x - 88x = 3080
  
  7x = 3080
  
  x = 440...so the number of bricks will be 440
  
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