Paige and Demi share 42 sweets in the ratio 3 : 2 : 1\n\nWork out the number of sweets that each of them receives.","markscheme":"- Sum of ratio parts: $3 + 2 + 1 = 6$ M1\n- Value per part: $42 \\div 6 = 7$ M1\n- Molly: $3 \\times 7 = 21$, Paige: $2 \\times 7 = 14$, Demi: $1 \\times 7 = 7$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Finds the total number of parts (6).","code":"M"},{"id":"p2","marks":1,"description":"Calculates the value of one part ($42 \\div 6 = 7$).","code":"M"},{"id":"p3","marks":1,"description":"Correctly identifies Molly: 21, Paige: 14, Demi: 7.","code":"A"}],"finalAnswers":["21, 14, 7"],"generatedAt":"2026-05-07T01:45:21.089Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"ratio_parts","label":"Share using ratio parts","steps":[{"type":"text","order":0,"title":"Add the ratio parts","content":"The ratio $3:2:1$ means the sweets are split into $3$, $2$ and $1$ equal-sized parts. Add the parts:\n\n$$3+2+1=6$$\n\nThis is the first method mark: there are $6$ equal parts altogether.","highlights":[{"text":"share 42 sweets in the ratio 3 : 2 : 1","location":"specification"}]},{"type":"text","order":1,"title":"Find one part","content":"The $42$ sweets make up all $6$ parts, so divide by $6$ to find the size of one part:\n\n$$42\\div6=7$$\n\nEach ratio part is worth $7$ sweets. This earns the second method mark.","highlights":[{"text":"share 42 sweets","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{Molly}=\\htmlData{anchor=molly_parts}{\\color{@sky}{3}}\\times\\htmlData{anchor=part_value_molly}{\\color{@amber}{7}}=\\htmlData{anchor=molly_total}{\\color{@green}{21}}"},{"latex":"\\text{Paige}=\\htmlData{anchor=paige_parts}{\\color{@sky}{2}}\\times\\htmlData{anchor=part_value_paige}{\\color{@amber}{7}}=\\htmlData{anchor=paige_total}{\\color{@green}{14}}"},{"latex":"\\text{Demi}=\\htmlData{anchor=demi_parts}{\\color{@sky}{1}}\\times\\htmlData{anchor=part_value_demi}{\\color{@amber}{7}}=\\htmlData{anchor=demi_total}{\\color{@green}{7}}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"molly_parts"},{"color":"green","style":"text-color","anchor":"molly_total"},{"color":"sky","style":"text-color","anchor":"paige_parts"},{"color":"green","style":"text-color","anchor":"paige_total"},{"color":"sky","style":"text-color","anchor":"demi_parts"},{"color":"green","style":"text-color","anchor":"demi_total"}]},"order":2,"title":"Multiply by each share","description":"Multiply the $7$ sweets in one part by each person's number of ratio parts.\n\nMolly receives $21$ sweets, Paige receives $14$ sweets and Demi receives $7$ sweets. These correct allocations earn the accuracy mark (A1)."}]}],"generatedAt":"2026-07-21T02:47:43.435Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":81,"sampleSize":89}},{"id":"a867577f-1069-4d1f-830a-30423ea7df13","revisionId":"8f9fa6b8-b7ac-4ab3-8d6c-93bb1ec188e9","questionNumber":"4","questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Ratio","calculatorUse":null,"parts":[{"id":"f41f45f4-227f-4fd2-9ac1-9d8fd7268b38","label":"0","content":"Carly and James share some money in the ratio 5 : 3\nCarly gets £70 more than James.\n\nWork out how much money James gets.","markscheme":"- Difference in parts: $5 - 3 = 2$ M1\n- Value of one part: $70 \\div 2 = 35$ M1\n- James's share: $3 \\times 35 = 105$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Identifies that the difference of 2 parts corresponds to £70.","code":"M"},{"id":"p2","marks":1,"description":"Calculates the value of one part as £35.","code":"M"},{"id":"p3","marks":1,"description":"Calculates James's total as £105.","code":"A"}],"finalAnswers":["105"],"generatedAt":"2026-05-07T01:45:21.089Z","modelVersion":"gemini-3-f

Ratio Questions

Ratio Questions

Ratio Questions

Ratio Questions