IMC 2020 Q12
12. Farmer Fatima rears chickens and goats. Today she returned from market and said, “I sold 80 animals, and now there are 200 fewer legs on my farm than before!”
How many goats did she sell?
- A 15
- B 20
- C 25
- D 30
- E 35
Intermediate Mathematical Challenge 2020, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 20
Let the number of chickens and goats sold be \(c\) and \(g\) respectively.
Then, since 80 animals are sold, we have \(c + g = 80\).
Also, \(2c + 4g = 200\), since the chickens have two legs and the goats have four legs.
Dividing the second equation by 2, we obtain \(c + 2g = 100\).
Then, subtracting the first equation gives \(g = 100 - 80 = 20\).
So 20 goats were sold.
Solution © UK Mathematics Trust, from the IMC 2020 solutions. Longer versions with investigations: Solutions and investigations (PDF).