1. **Question 2: Molly, Paige and Demi share 42 sweets in the ratio 3 : 2 : 1.** Step 1: Add the parts of the ratio: $3 + 2 + 1 = 6$ parts total. Step 2: Find the value of one part: $\frac{42}{6} = 7$ sweets per part. Step 3: Calculate sweets for each: - Molly: $3 \times 7 = 21$ sweets - Paige: $2 \times 7 = 14$ sweets - Demi: $1 \times 7 = 7$ sweets 2. **Question 3: ABC is a straight line. Length BC is three times AB, and AC = 80 metres. Find BC.** Step 1: Let length AB = $x$. Step 2: Then BC = $3x$. Step 3: Total length AC = AB + BC = $x + 3x = 4x$. Step 4: Given AC = 80, so $4x = 80$. Step 5: Solve for $x$: $x = \frac{80}{4} = 20$ metres. Step 6: Find BC: $3x = 3 \times 20 = 60$ metres. 3. **Question 4: Carly and James share money in ratio 5 : 3. Carly gets 70 more than James. Find James' amount.** Step 1: Let James' amount be $x$. Step 2: Carly's amount is $x + 70$. Step 3: Ratio gives $\frac{x + 70}{x} = \frac{5}{3}$. Step 4: Cross multiply: $3(x + 70) = 5x$. Step 5: Expand: $3x + 210 = 5x$. Step 6: Rearrange: $210 = 5x - 3x = 2x$. Step 7: Solve for $x$: $x = \frac{210}{2} = 105$. James gets 105. 4. **Question 5: Jerry and Mick share money in ratio 2 : 3. Mick gets 900. Find Jerry's amount.** Step 1: Let Jerry's amount be $x$. Step 2: Mick's amount is $900$. Step 3: Ratio: $\frac{x}{900} = \frac{2}{3}$. Step 4: Cross multiply: $3x = 2 \times 900 = 1800$. Step 5: Solve for $x$: $x = \frac{1800}{3} = 600$. Jerry gets 600. 5. **Question 6: Ali and Steve share sweets in ratio 2 : 7. Steve gets 30 more sweets than Ali. Find Steve's amount.** Step 1: Let Ali's sweets be $2x$, Steve's sweets be $7x$. Step 2: Difference: $7x - 2x = 5x = 30$. Step 3: Solve for $x$: $x = \frac{30}{5} = 6$. Step 4: Steve's sweets: $7x = 7 \times 6 = 42$. 6. **Question 7: Dave mixes flour, butter and sugar in ratio 6 : 4 : 1. Uses 160g butter. Find flour and sugar amounts.** Step 1: Butter corresponds to 4 parts = 160g. Step 2: One part = $\frac{160}{4} = 40$ grams. Step 3: Flour = $6 \times 40 = 240$ grams. Step 4: Sugar = $1 \times 40 = 40$ grams. 7. **Question 8: Alvin and Simon share 540 in ratio 4 : 5. Alvin gives half his share to Theo, Simon gives a tenth of his share to Theo. Find fraction Theo receives.** Step 1: Total parts = $4 + 5 = 9$. Step 2: One part = $\frac{540}{9} = 60$. Step 3: Alvin's share = $4 \times 60 = 240$. Step 4: Simon's share = $5 \times 60 = 300$. Step 5: Alvin gives half: $\frac{1}{2} \times 240 = 120$. Step 6: Simon gives a tenth: $\frac{1}{10} \times 300 = 30$. Step 7: Theo receives $120 + 30 = 150$. Step 8: Fraction of total: $\frac{150}{540} = \frac{5}{18}$. 8. **Question 9: ABC is a straight line. BC is 4 times AB. BC = 100m. Find AC.** Step 1: Let AB = $x$. Step 2: BC = $4x = 100$. Step 3: Solve for $x$: $x = \frac{100}{4} = 25$. Step 4: AC = AB + BC = $25 + 100 = 125$ metres. 9. **Question 10: Bob mixes red, yellow, white paint in ratio 5 : 4 : 1 to make 750 ml. Has 400 ml red, 300 ml yellow, 200 ml white. Does he have enough?** Step 1: Total parts = $5 + 4 + 1 = 10$. Step 2: One part = $\frac{750}{10} = 75$ ml. Step 3: Required amounts: - Red: $5 \times 75 = 375$ ml - Yellow: $4 \times 75 = 300$ ml - White: $1 \times 75 = 75$ ml Step 4: Compare with available: - Red: has 400 ml, needs 375 ml → enough - Yellow: has 300 ml, needs 300 ml → enough - White: has 200 ml, needs 75 ml → enough Step 5: Conclusion: Bob has enough paint. 10. **Question 11: Megan mixes 2 parts fruit juice with 5 parts sparkling water. Has 180 ml juice and 400 ml water. Find greatest amount of drink she can make.** Step 1: Total parts = $2 + 5 = 7$. Step 2: Amount per part from juice: $\frac{180}{2} = 90$ ml. Step 3: Amount per part from water: $\frac{400}{5} = 80$ ml. Step 4: Limiting factor is smaller part amount = 80 ml. Step 5: Total drink = $7 \times 80 = 560$ ml. 11. **Question 12: Probability of red counter is 0.35. Blue : White counters = 2 : 3. Complete probability table.** Step 1: Total probability = 1. Step 2: Probability red = 0.35. Step 3: Let probability blue = $2x$, white = $3x$. Step 4: Sum: $0.35 + 2x + 3x = 1$ → $0.35 + 5x = 1$. Step 5: Solve for $x$: $5x = 0.65$ → $x = 0.13$. Step 6: Blue = $2 \times 0.13 = 0.26$. Step 7: White = $3 \times 0.13 = 0.39$. 12. **Question 13: Al, Tom, Joe share 3000. Al : Tom = 5 : 4, Joe = 1.5 × Tom. Find Tom's amount.** Step 1: Let Tom's amount = $x$. Step 2: Al's amount = $\frac{5}{4}x$. Step 3: Joe's amount = $1.5x = \frac{3}{2}x$. Step 4: Total: $\frac{5}{4}x + x + \frac{3}{2}x = 3000$. Step 5: Convert to common denominator 4: $\frac{5}{4}x + \frac{4}{4}x + \frac{6}{4}x = \frac{15}{4}x = 3000$. Step 6: Solve for $x$: $x = \frac{3000 \times 4}{15} = 800$. Tom gets 800. 13. **Question 14: Harry and Gary have 300 stickers. Ratio Harry : Gary = 7 : 3. After giving some, ratio is 8 : 7. Find how many stickers Harry gives Gary.** Step 1: Let initial parts be $7x$ and $3x$, total $10x = 300$ → $x=30$. Step 2: Harry has $210$, Gary has $90$. Step 3: Let Harry gives $y$ stickers to Gary. Step 4: New amounts: Harry $210 - y$, Gary $90 + y$. Step 5: New ratio: $\frac{210 - y}{90 + y} = \frac{8}{7}$. Step 6: Cross multiply: $7(210 - y) = 8(90 + y)$. Step 7: $1470 - 7y = 720 + 8y$. Step 8: $1470 - 720 = 8y + 7y$ → $750 = 15y$. Step 9: $y = 50$. Harry gives 50 stickers. 14. **Question 15: Small and large chocolate bars sold in packs 4 and 9. Packs sold ratio 5 : 2. Total bars sold 190. Find number of small bars sold.** Step 1: Let packs small = $5x$, packs large = $2x$. Step 2: Total bars: $4 \times 5x + 9 \times 2x = 20x + 18x = 38x$. Step 3: $38x = 190$ → $x = \frac{190}{38} = 5$. Step 4: Small bars sold: $4 \times 5x = 4 \times 25 = 100$. 15. **Question 16: Dermot has 240 counters: 15% red, 2/5 blue, yellow:green = 3:1. Find yellow counters.** Step 1: Red counters: $15\%$ of 240 = $0.15 \times 240 = 36$. Step 2: Blue counters: $\frac{2}{5} \times 240 = 96$. Step 3: Remaining counters: $240 - 36 - 96 = 108$ (yellow + green). Step 4: Ratio yellow:green = 3:1, total parts = 4. Step 5: One part = $\frac{108}{4} = 27$. Step 6: Yellow counters = $3 \times 27 = 81$. 16. **Question 17: Daisy bakes 180 cakes: 20% chocolate, 4/9 vanilla, banana:lemon = 3:5. Find lemon cakes.** Step 1: Chocolate cakes: $20\%$ of 180 = $36$. Step 2: Vanilla cakes: $\frac{4}{9} \times 180 = 80$. Step 3: Remaining cakes: $180 - 36 - 80 = 64$ (banana + lemon). Step 4: Ratio banana:lemon = 3:5, total parts = 8. Step 5: One part = $\frac{64}{8} = 8$. Step 6: Lemon cakes = $5 \times 8 = 40$. 17. **Question 18: Angelina earns 1800 monthly, saves 30%, spends rest. Rent : other expenses = 4 : 5. Find rent amount.** Step 1: Amount spent = $70\%$ of 1800 = $0.7 \times 1800 = 1260$. Step 2: Total parts = $4 + 5 = 9$. Step 3: One part = $\frac{1260}{9} = 140$. Step 4: Rent = $4 \times 140 = 560$. 18. **Question 19: Red and green counters ratio 2 : 3. Red counters = 28. Find total counters.** Step 1: Let red = $2x = 28$. Step 2: Solve for $x$: $x = 14$. Step 3: Green = $3x = 42$. Step 4: Total = $28 + 42 = 70$. 19. **Question 20: Clara and Dawn stamps ratio 5 : 9. Dawn has 36 more stamps. Find Clara's stamps.** Step 1: Let Clara = $5x$, Dawn = $9x$. Step 2: Difference: $9x - 5x = 4x = 36$. Step 3: Solve for $x$: $x = 9$. Step 4: Clara's stamps = $5 \times 9 = 45$. 20. **Question 21: Counters red:blue:yellow = 4:5:8. Yellow is 24 more than blue. Find total counters.** Step 1: Let common multiplier be $x$. Step 2: Yellow - Blue = $8x - 5x = 3x = 24$. Step 3: Solve for $x$: $x = 8$. Step 4: Total counters = $(4 + 5 + 8) \times 8 = 17 \times 8 = 136$. 21. **Question 22: Cameron has 2p and 5p coins in ratio 2 : 3. Total value 95p. Find number of 5p coins.** Step 1: Let number of 2p coins = $2x$, 5p coins = $3x$. Step 2: Total value: $2 \times 2x + 5 \times 3x = 4x + 15x = 19x$ pence. Step 3: $19x = 95$ → $x = 5$. Step 4: Number of 5p coins = $3x = 15$. 22. **Question 23: 8 pencils cost 1.92. Pen:pencil cost ratio 4:3. Find cost of 5 pens.** Step 1: Cost per pencil = $\frac{1.92}{8} = 0.24$. Step 2: Pen cost = $\frac{4}{3} \times 0.24 = 0.32$. Step 3: Cost of 5 pens = $5 \times 0.32 = 1.60$. 23. **Question 24: Triangle ABC with angles 83° at B, 52° at A, ADB straight line. Angle BCD : ACD = 2 : 3. Find angle ADC.** Step 1: Sum of angles in triangle ABC: $180°$. Step 2: Angle C = $180° - 83° - 52° = 45°$. Step 3: Let angle BCD = $2k$, angle ACD = $3k$. Step 4: Since BCD + ACD = angle C, $2k + 3k = 45°$ → $5k = 45°$ → $k = 9°$. Step 5: Angle ADC = angle ACD = $3k = 27°$. **Final answers:** Q2: Molly 21, Paige 14, Demi 7 Q3: BC = 60 m Q4: James = 105 Q5: Jerry = 600 Q6: Steve = 42 Q7: Flour = 240 g, Sugar = 40 g Q8: Theo receives $\frac{5}{18}$ of total Q9: AC = 125 m Q10: Yes, enough paint Q11: 560 ml Q12: Blue 0.26, White 0.39 Q13: Tom = 800 Q14: Harry gives 50 stickers Q15: Small bars = 100 Q16: Yellow = 81 Q17: Lemon = 40 Q18: Rent = 560 Q19: Total counters = 70 Q20: Clara = 45 Q21: Total counters = 136 Q22: 5p coins = 15 Q23: Cost of 5 pens = 1.60 Q24: Angle ADC = 27°