Impossible Eggs

Algebra Level 3

If one-and-a-half chickens can lay one-and-a-half eggs in one-and-a-half days, how many eggs can a dozen chickens lay in one week?


The answer is 56.

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2 solutions

Delano Might
Oct 12, 2015

The rate at which each chicken lays eggs is

l a y i n g r a t e = 1.5 e g g s 1.5 c h i c k e n s × 1.5 d a y s = 2 3 e g g s p e r c h i c k e n p e r d a y laying\quad rate\quad =\quad \frac { 1.5\quad eggs }{ 1.5\quad chickens\quad \times \quad 1.5\quad days } \quad =\quad \frac { 2 }{ 3 } \quad eggs\quad per\quad chicken\quad per\quad day

Then, for 12 chickens in 7 days,

n u m b e r o f e g g s = 2 3 e g g s p e r c h i c k e n p e r d a y × 12 c h i c k e n s × 7 d a y s n u m b e r o f e g g s = 56 number\quad of\quad eggs\quad =\quad \cfrac { 2 }{ 3 } \quad eggs\quad per\quad chicken\quad per\quad day\quad \times \quad 12\quad chickens\quad \times \quad 7\quad days\\ \boxed { number\quad of\quad eggs\quad =\quad 56 }

Beautiful. Thanks.

Damian Howison - 5 years, 8 months ago
Damian Howison
Oct 9, 2015

(Chickens, Eggs, Days) (1.5, 1.5, 1.5) (3, 3, 1.5) (12, 12, 1.5) (12, 24, 3) (12, 8, 1) (12, 56, 7)

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