1. **Problem:** Mrs Gibson bought $x$ pencils and distributed them equally among 40 students. How many pencils did each student receive? 2. **Formula:** To find the number of pencils each student receives, divide the total pencils by the number of students. $$\text{Pencils per student} = \frac{x}{40}$$ 3. **Explanation:** Since the pencils are shared equally, each student gets an equal fraction of the total pencils. 4. **Answer:** Each student receives $$\frac{x}{40}$$ pencils. 2. **Problem:** Jessica buys 10 dresses, each costing $y$. How much must she pay in all? 3. **Formula:** Total cost is number of dresses times cost per dress. $$\text{Total cost} = 10 \times y = 10y$$ 4. **Answer:** Jessica must pay $$10y$$. 3. **Problem:** Alan was $m$ years old 2 years ago. How old is he this year? 4. **Formula:** Current age is age 2 years ago plus 2. $$\text{Current age} = m + 2$$ 5. **Answer:** Alan is $$m + 2$$ years old this year. 4. **Problem:** Sue bought $z$ apples and gave 5 apples to her friends. How many apples had she left? 5. **Formula:** Remaining apples = total apples - apples given away. $$\text{Apples left} = z - 5$$ 6. **Answer:** Sue has $$z - 5$$ apples left. 5. **Problem:** Mindy obtained 88 marks, Sandy obtained $x$ marks. What was their average marks? 6. **Formula:** Average = sum of marks divided by number of students. $$\text{Average} = \frac{88 + x}{2}$$ 7. **Answer:** Their average marks is $$\frac{88 + x}{2}$$. 6. **Problem:** Gordon has $n$ stamps, Mike has twice as many as Gordon, Kenny has thrice as many as Mike. How many stamps do they have altogether? 7. **Formula:** Total stamps = Gordon's + Mike's + Kenny's $$\text{Mike's stamps} = 2n$$ $$\text{Kenny's stamps} = 3 \times 2n = 6n$$ $$\text{Total} = n + 2n + 6n = 9n$$ 8. **Answer:** They have $$9n$$ stamps altogether. 7. **Problem:** Belinda had 50. She gave half to her sister, then her mother gave her $a$. How much money did Belinda have in the end? 8. **Formula:** Half of 50 is 25 given away, so left with 25. Then add $a$. $$\text{Money left} = 50 - \frac{50}{2} + a = 50 - 25 + a$$ Intermediate step with cancellation: $$50 - \cancel{\frac{50}{2}} + a = 50 - 25 + a$$ 9. **Answer:** Belinda has $$25 + a$$ in the end. 8. **Problem:** Joy has $x$ balloons, Maggie has $y$ balloons, Helen has 5 balloons. How many balloons do they have in all? 9. **Formula:** Total balloons = $x + y + 5$ 10. **Answer:** They have $$x + y + 5$$ balloons in all. 9. **Problem:** Nancy baked $z$ cakes, gave 5 to neighbors and 12 to relatives. How many cakes had she left? 10. **Formula:** Cakes left = total cakes - (cakes given to neighbors + cakes given to relatives) $$\text{Cakes left} = z - (5 + 12) = z - 17$$ 11. **Answer:** Nancy has $$z - 17$$ cakes left. 10. **Problem:** Felicia’s car consumed $x$ litres of petrol on Monday, twice that on Tuesday. She pumped 60 litres before Monday. How much petrol was left? 11. **Formula:** Total petrol consumed = $x + 2x = 3x$ Petrol left = initial petrol - total consumed $$\text{Petrol left} = 60 - 3x$$ 12. **Answer:** Felicia has $$60 - 3x$$ litres of petrol left.