The square root of half a swarm of bees have flown into a bush while
eight-ninths of the swarm of bees stay outside of the bush. A female bee is
helping a male bee that is stuck in a flower. How many bees are there in
the swarm?
Answer
Let x be the total number of bees in the swarm.
x - sqrt of (x/2) - 8x/9 - 2 = 0
x - 8x/9 - 2 = sqrt of (x/2)
x/9 - 2 = sqrt of (x/2)
Square both sides
(x/9 - 2)² = (sqrt of (x/2))²
x²/81 - 4x/9 + 4 = x/2
x²/81 - 4x/9 - x/2 + 4 = 0
(2x² - 72x - 81x + 648)/162 = 0
2x² - 153x + 648 = 0
(2x - 9)(x - 72) = 0
x = 4.5 or x = 72 Only 72 is the correct answer.
