Birds of the same feather flock together

Algebra Level 3

There are male and female doves on a fence. When 5 male doves leave, there remain 2 female doves for every male dove. Then 25 female doves leave, there are now 3 male doves for every female dove. Find the original number of male doves.

34 30 10 8 20 15 25

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2 solutions

Chew-Seong Cheong
Oct 30, 2017

Let the original numbers of male and female doves on the fence be m m and f f respectively. Then we have:

f = 2 ( m − 5 ) 3 ( f − 25 ) = m − 5 Note that f = 2 ( m − 5 ) 3 ( 2 m − 10 − 25 ) = m − 5 6 m − 105 = m − 5 5 m = 100 ⟹ m = 20 \begin{aligned} f & = 2(m-5) \\ 3({\color{#3D99F6} f}-25) & = m-5 & \small \color{#3D99F6} \text{Note that }f= 2(m-5) \\ 3({\color{#3D99F6} 2m-10}-25) & = m-5 \\ 6m - 105 & = m - 5 \\ 5m & = 100 \\ \implies m & = \boxed{20} \end{aligned}

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m − 5 f = 1 2 \dfrac{m-5}{f}=\dfrac{1}{2} ⟹ \implies 1 \color{#D61F06}\boxed{1}

m − 5 f − 25 = 3 1 \dfrac{m-5}{f-25}=\dfrac{3}{1} ⟹ \implies 2 \color{#D61F06}\boxed{2}

From 1 \color{#D61F06}\boxed{1} , we get f = 2 m − 10 f=2m-10 . Substitute f f in 2 \color{#D61F06}\boxed{2} .

m − 5 2 m − 10 − 25 = 3 \dfrac{m-5}{2m-10-25}=3

m − 5 = 6 m − 30 − 75 m-5=6m-30-75

100 = 5 m 100=5m

20 = m \boxed{20=m}

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