1. Problem 14: Yuki's cookies Yuki baked some cookies on Monday. Half were eaten on Tuesday by friends, then Yuki ate 3 on Wednesday, took 2 to school on Thursday, and 7 remained on Friday. We want to find how many cookies she baked on Monday. 2. Define the variable: Let $x$ be the number of cookies baked on Monday. 3. Write the equation based on the problem: After Tuesday, half the cookies remain: $\frac{x}{2}$. On Wednesday, Yuki ate 3, so cookies left: $\frac{x}{2} - 3$. On Thursday, she took 2 more: $\frac{x}{2} - 3 - 2 = \frac{x}{2} - 5$. On Friday, 7 cookies remain, so: $$\frac{x}{2} - 5 = 7$$ 4. Solve the equation: Add 5 to both sides: $$\frac{x}{2} - 5 + 5 = 7 + 5$$ $$\frac{x}{2} = 12$$ Multiply both sides by 2: $$\cancel{2} \times \frac{x}{\cancel{2}} = 12 \times 2$$ $$x = 24$$ 5. Answer for problem 14: Yuki baked 24 cookies on Monday. 6. Problem 15: Student's money A student has 45 initially, receives 25 and 15 more, then spends 40 on shoes. Find how much money she has left. 7. Write the number sentence: $$45 + 25 + 15 - 40 = ?$$ 8. Simplify addition first: $$45 + 25 = 70$$ $$70 + 15 = 85$$ 9. Subtract the cost of shoes: $$85 - 40 = 45$$ 10. Answer for problem 15: The student has 45 left after buying the shoes.