Mathematics
Mathematics
Problem
Chewbacca has 20 pieces of cherry gum and 30 pieces of grape gum. Some of the pieces are in complete packs, while others are loose. Each complete pack has exactly pieces of gum. If Chewbacca loses one pack of cherry gum, then the ratio of the number of pieces of cherry gum he has to the number of pieces of grape gum will be exactly the same as if he instead finds 5 packs of grape gum. Find .Intuitive explanation
The key insight is that two different scenarios—losing cherry packs and gaining grape packs—produce the same ratio of cherry to grape gum. Set up equations for each scenario, then use the fact that these ratios are equal to solve for . This is a classic "two paths, one outcome" problem where algebra forces the unknown to reveal itself.
Intuitive explanation
The key insight is that two different scenarios—losing cherry packs and gaining grape packs—produce the same ratio of cherry to grape gum. Set up equations for each scenario, then use the fact that these ratios are equal to solve for . This is a classic "two paths, one outcome" problem where algebra forces the unknown to reveal itself.