how many birds where there at first

Question

• A flock of birds left to go to Africa together.
• Half went astray in fog.
• One Eight are lost in a sandstorm.
• 6 are killed
• Finally 42 arrive safely to Africa.

Answer 1

Let x = number of birds there at first

 

"Half [of original number] went astray in fog"     means (1/2)x

"One Eight [of original number] are lost in a sandstorm"       means (1/8)x

"6 are killed"                means 6

"42 arrive safely to Africa"           means 42

 

The original number (that is, x) minus those lost equals those who arrived safely:

        x - (1/2)x - (1/8)x - 6 = 42

        8x - 4x - x - 48 = 336         [multiply my LCD=8]

          3x = 384                 [collect terms; add 48 to both sides]

           x = 128              [divide both sides by 3]

 

There were 128 birds at the start.

 

Check:

       A flock of birds left to go to Africa together.    128 birds at the start
      Half went astray in fog.        128 - 64 leaves 64.
      One Eight are lost in a sandstorm.       64 - 16 = 48 left.
      6 are killed                                         48 - 6 = 42 left.
      Finally 42 arrive safely to Africa.         Yes !! 42 made it.