Problem K. 674. (December 2020)
K. 674. In the backyard of aunt Ann, there are 120 animals: brown hens, white ducks, brown pigs and white rabbits. The number of white animals is 64, and the number of two-legged animals is 84. There are twice as many brown hens as white rabbits. How many of each species of animal live in aunt Ann's backyard?
(6 pont)
Deadline expired on January 11, 2021.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. Írjuk egy táblázatba az adatokat.
A barna állatok száma \(\displaystyle 120-64=56\), a négylábúak száma pedig \(\displaystyle 120-84=36\).
| barna tyúk | barna malac | \(\displaystyle 56\) |
| fehér kacsa | fehér nyúl | \(\displaystyle 64\) |
| \(\displaystyle 84\) | \(\displaystyle 36\) |
Legyen \(\displaystyle x\) a fehér nyulak száma, ekkor a barna tyúkokból \(\displaystyle 2x\) van és a fehér kacsákból \(\displaystyle 64-x\).
| \(\displaystyle 2x\) | \(\displaystyle 56-2x\) | \(\displaystyle 56\) |
| \(\displaystyle 64-x\) | \(\displaystyle x\) | \(\displaystyle 64\) |
| \(\displaystyle 84\) | \(\displaystyle 36\) |
A kétlábú állatok száma \(\displaystyle 2x + (64-x) = 84\), ahonnan \(\displaystyle x = 20\). (Ekkor nyilván \(\displaystyle 56-2x+x=36\) is teljesül.) A fehér nyulak száma \(\displaystyle 20\), a barna tyúkoké \(\displaystyle 40\), a barna malacoké \(\displaystyle 16\), a fehér kacsáké pedig \(\displaystyle 44\).
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144 students sent a solution. 6 points: 118 students. 5 points: 8 students. 4 points: 3 students. 3 points: 1 student. 2 points: 3 students. 1 point: 2 students. Unfair, not evaluated: 8 solutionss. Not shown because of missing birth date or parental permission: 1 solutions.
Problems in Mathematics of KöMaL, December 2020