IMC 2016 Q6
6. One third of the animals in Jacob's flock are goats, the rest are sheep. There are twelve more sheep than goats.
How many animals are there altogether in Jacob's flock?
- A 12
- B 24
- C 36
- D 48
- E 60
Intermediate Mathematical Challenge 2016, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 36
Let \(g\) and \(s\) be the number of goats and sheep respectively. Then \(s = 2g\) and \(12 = s - g = 2g - g = g\). Hence the number of animals is \(s + g = 3g = 36\).
Solution © UK Mathematics Trust, from the IMC 2016 solutions. Longer versions with investigations: Solutions and investigations (PDF).