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Algebra Difficulty 4.2 AIME Find the answer North Macedonia

There were 25 birds on two branches. After a while 5 birds from the first branch flew over to the second and after a while longer 7 birds from the second flew away. In that moment on the first branch there were twice as many birds than on the second. How many birds were there on each of the two branches in the beginning?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

When the 7 birds flew away from the second branch the total number of birds on both branches was 257=1825-7=18. Because in that moment on the first branch there were twice as many birds than on the second, there were 18:3=618:3=6 birds on the second branch, and on the first one were 26=122 \cdot 6=12 birds. Hence, before the 7 birds flew away from the second branch, there were 6+7=136+7=13 birds on it. In the beginning, before the 5 birds flew from the first to the second branch, on the second branch were 135=813-5=8 birds and on the first were 12+5=1712+5=17 birds.

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