Billy has three times as many llamas as lambs.  Milly has twice as many lambs as llamas.  They have $$17$$ animals in total.  How many of the animals are llamas? 
Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Indefinite Equation Word Problems
Let Billy have $$b$$ lambs and $$3b$$ llamas. Let Milly have $$m$$ llamas and $$2m$$ lambs.  Therefore, as they have $$17$$ animals in total, $$4b + 3m= 17$$. The only positive integer solution of this equation is $$b= 2$$, $$m= 3$$. So the number of llamas is $$3b + m = 3 \times 2 + 3 = 6 + 3 = 9$$. 