1. Problem: Write expressions for the length of red and blue ribbons based on given conditions. 2. The problem states: The length of the red ribbon is 7 inches less than the length of the blue ribbon. 3. Formula: If $b$ is the length of the blue ribbon, then the length of the red ribbon $r$ is given by: $$r = b - 7$$ 4. a. Calculate red ribbon length for given blue ribbon lengths: - For $b=10$ inches: $$r = 10 - 7 = 3$$ inches - For $b=27$ inches: $$r = 27 - 7 = 20$$ inches - For $b=x$ inches: $$r = x - 7$$ inches 5. b. Find blue ribbon length if red ribbon is 12 inches: Given $r=12$, use $r = b - 7$: $$12 = b - 7$$ Add 7 to both sides: $$12 + 7 = b$$ $$\cancel{12} + 7 = b$$ $$19 = b$$ inches 6. Problem: Tyler has 3 times as many books as Mai. 7. Formula: If $m$ is the number of books Mai has, and $t$ is the number Tyler has: $$t = 3m$$ 8. a. Find Mai's books for given Tyler's books: - For $t=15$: $$15 = 3m$$ Divide both sides by 3: $$\frac{15}{\cancel{3}} = m$$ $$5 = m$$ books - For $t=21$: $$21 = 3m$$ Divide both sides by 3: $$\frac{21}{\cancel{3}} = m$$ $$7 = m$$ books - For $t=x$: $$x = 3m$$ Divide both sides by 3: $$\frac{x}{3} = m$$ books 9. b. Tyler has 18 books, find Mai's books: $$18 = 3m$$ Divide both sides by 3: $$\frac{18}{\cancel{3}} = m$$ $$6 = m$$ books Final answers: - Red ribbon lengths: 3 inches, 20 inches, $x-7$ inches - Blue ribbon length when red is 12 inches: 19 inches - Mai's books: 5, 7, $\frac{x}{3}$, and 6 books