At the local Sunday school meeting, the teacher brought in some puppies. There were 20 more children than puppies. In the corner of the room, within the ant’s nest, there were exactly 10 times as many ants as children. In total, including the teacher, the children, the puppies and the ants, there were 1440 legs in the room. How many children attended?
Answer
23 children (46 legs): with 230 ants (1380 legs), 3 puppies (12 legs) and 1 teacher (2 legs). If we call the number of puppies P, then there were (P + 20) children and 10 x (P + 20) ants, and a single teacher. If we now count the legs, we get:
Puppies : P x 4 = 4P
Children: (P + 20) x 2 = 2P + 40
Ants : 10 x (P + 20) x 6 = 60P + 1200
Teacher : 2 = 2
66P + 1242
Giving 66P + 1242 = 1440, which means that P = 3, so there were 3 puppies, hence 23 children.