Struggle for Equality

Algebra Level 2

A certain number of birds are sitting on two trees $A$ and $B$ . The birds on tree $A$ said to the birds on tree $B$ that if one of you join us than we would be twice in number than you. The birds on tree B replied that instead if one of you join us then we would become equal in number. If the number of birds on trees $A$ and $B$ are $x$ and $y$ respectively, what is the value of $x+y$ ?

The answer is 12.

1 solution

Hung Woei Neoh
May 19, 2016

Transform the sentences into equations:

$x+1 = 2(y-1) \implies$ Eq.(1)

$x-1=y+1$

$x=y+2 \implies$ Eq.(2)

Substitute Eq.(2) into Eq.(1):

$y+2+1 = 2(y-1)\\ y+3=2y-2\\ y=5\\ x=5+2=7\\ x+y=7+5=\boxed{12}$

Struggle for Equality

The answer is 12.

1 solution

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