Question

Carter and his cousin are playing a game where they pick up coloured sticks. Carter currently has 30 points and likes to pick up the red sticks, earning 2 points every turn. His cousin just lost all his points on the previous turn, and has a strategy to catch up by getting all the purple ones, earning 5 points per turn. In a certain number of turns, the score will be tied. How many points will they each have?

Answer 1

30+2r = 5p
since 30 and 5p are both multiples of 5, 2r must also be a multiple of 5, let r=5, so they each have 40 points