Birds

Algebra Level 2

There are two sets of birds on different branches: say group A and group B.

One of the group A says if one of you ( group B ) will come to us, then we will be twice number of you, then one of the group B says: no, no, if one of you ( group A ) will come to us , then we will be equal to you.

Find the number of birds in A and number of birds in B

type your answer like this:
xy ( without any space, without any comma )
( x represents number of A birds ...y represents number of B birds )

The answer is 75.

2 solutions

Noel Lo
Jun 3, 2016

A has twice the number of birds as B so A has $\frac{2}{3}$ the total number of birds while B has $\frac{1}{3}$ . If A and B have an equal number, each has half. This means a difference of $\frac{1}{6}$ in each nest. Observe also that one bird from A to B and one bird from B to A means a difference of two birds in each nest. So onesixth is equal to two birds which means there are a dozen birds in all. It is now easy to see that A has seven while B has five.

Hung Woei Neoh
May 25, 2016

This is exactly the same as this question . Anyway...

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):

$y+2+1 = 2(y-1)\\ y+3=2y-2\\ y=5\\ x=5+2=7$

The answer is entered in the form of $\overline{xy}$ , which is $\boxed{75}$

Birds

The answer is 75.

2 solutions

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