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We need to reverse this percentage to find the original price.","highlights":[{"text":"increased by 4%","location":"specification"},{"text":"increased by £152.20","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=fourpercent}{\\color{@sky}{4\\%}}=\\htmlData{anchor=increase}{\\color{@sky}{\\pounds152.20}}\\quad\\text{(M1)}"},{"latex":"\\htmlData{anchor=onepercent}{\\color{@green}{1\\%}}=\\htmlData{anchor=onevalue}{\\color{@green}{\\pounds38.05}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"fourpercent"},{"color":"green","style":"text-color-with-background","anchor":"onevalue"}],"connections":[{"to":"onevalue","from":"increase","color":"sky","label":"divide by 4","style":"solid"}]},"order":1,"title":"Find 1%","description":"M1: equate the 4% increase to £152.20. Then divide by 4 to find the value of 1%."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=onepercent}{\\color{@green}{1\\% = \\pounds 38.05}}"},{"latex":"\\htmlData{anchor=whole}{\\color{@orange}{100\\% = \\pounds 38.05 \\times 100}}"},{"latex":"\\htmlData{anchor=answer}{\\boxed{\\color{@orange}{\\pounds 3805}}}\\quad\\text{A1}"}],"highlights":[{"color":"green","style":"text-color","anchor":"onepercent"},{"color":"orange","style":"text-color-with-background","anchor":"whole"},{"color":"orange","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"whole","from":"onepercent","color":"orange","label":"multiply by 100","style":"solid"}]},"order":2,"title":"Find original price","description":"The original price represents 100%, so multiply the value of 1% by 100. Writing £3805 earns A1."}]}],"generatedAt":"2026-07-21T03:57:32.610Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":78},"walkthroughVideo":null},{"id":"b80bd1d6-5402-4285-96e3-838f92a3a79c","revisionId":"c325f3e0-e260-4b02-baef-8695885755af","questionNumber":"8","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Reverse Percentages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"0f712357-4818-4a0d-85d8-25e1f6fefad0","label":"0","content":"In a sale, the normal price of a car is reduced by 30%. \nThe sale price of the car is £6300\n\nWork out the normal price of the car.","markscheme":"- Award method mark for $6300 \\div 0.7$ or equating 70% to 6300 M1\n- Final answer of 9000 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Recognises that 70% corresponds to £6300 or uses the multiplier 0.7 in a division.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 9000.","code":"A"}],"finalAnswers":["9000"],"generatedAt":"2026-05-07T01:57:05.230Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"reverse_percentage","label":"Reverse the percentage","steps":[{"type":"text","order":0,"title":"Find the percentage left","content":"A reduction of $30\\%$ means the sale price is the remaining $70\\%$ of the normal price.\n\n$$100\\%-30\\%=70\\%$$","highlights":[{"text":"reduced by 30%","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=percent}{\\color{@sky}{70\\%}}=\\frac{70}{100}"},{"latex":"\\frac{70}{100}=\\htmlData{anchor=decimal}{\\color{@sky}{0.7}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"percent"}]},"order":1,"title":"Convert the percentage","description":"A 30% reduction leaves 70% of the normal price. Convert this percentage to a decimal before using it."},{"type":"text","order":2,"title":"Form the calculation","content":"The sale price is $70\\%$, or $0.7$, of the normal price. Divide by $0.7$ to find the whole amount:\n\n$$\\text{normal price}=6300\\div0.7$$\n\nWriting this calculation earns the method mark.","highlights":[{"text":"The sale price of the car is £6300","location":"specification"}]},{"type":"text","order":3,"title":"Evaluate the division","content":"$$$6300\\div0.7=9000$$\n\nSo the normal price is **£9000**. This correct final answer earns the accuracy mark."}]}],"generatedAt":"2026-07-21T03:55:11.230Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":88},"walkthroughVideo":null},{"id":"68ab67c9-e045-410b-bebc-3568543dfc20","revisionId":"71f04a18-2f45-4b95-9a3f-1bb50e1b0dc3","questionNumber":"9","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Reverse Percentages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"6f6927a1-1cd7-42ed-a9c5-05bc9f69535d","label":"0","content":"In a sale, normal prices are reduced by 15%. \nThe normal price of a pen is reduced by £1.20\n\nWork out the normal price of the pen.","markscheme":"- Award method mark for equating 15% to 1.20 or $1.20 \\div 0.15$ M1\n- Final answer of 8 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Identifies that 15% is equal to £1.20.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 8.","code":"A"}],"finalAnswers":["8"],"generatedAt":"2026-05-07T01:57:05.230Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"percentage_method","label":"Use the percentage","steps":[{"type":"text","order":0,"title":"Convert the percentage","content":"The £1.20 reduction is **15% of the normal price**. Let the normal price be $P$. Convert $15\\%$ to a decimal: $15\\%=0.15$. To find the whole amount from a percentage, divide by $0.15$.","highlights":[{"text":"normal prices are reduced by 15%.","location":"specification"},{"text":"reduced by £1.20","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=equation}{\\color{@sky}{1.20}=\\color{@amber}{0.15P}}"},{"latex":"\\htmlData{anchor=division}{\\frac{1.20}{0.15}=P}"},{"latex":"\\htmlData{anchor=answer}{P=\\pounds 8}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"equation"},{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"division","from":"equation","color":"sky","label":"divide both sides by 0.15","style":"solid"}]},"order":1,"title":"Divide by percentage","description":"Let P be the normal price. Since 15% of P is £1.20, divide both sides by 0.15. Setting £1.20 equal to 15% of P earns M1; finding £8 earns A1."}]}],"generatedAt":"2026-07-21T03:58:54.425Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":86},"walkthroughVideo":null}],"subjectCode":"igcse_maths__cie","summaries":[{"id":"89aff0e5-bc5f-429d-8e11-d5be7f0ebb10","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"4d5b3a51-d9ba-45ab-9c2d-0f10a9e5a022","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"a194fcc6-9401-49fd-879e-bf0709810754","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"3794d92d-ea51-46b5-ba4b-71dad3a02adc","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"18db6891-21c9-4d67-88ae-625c52c418f6","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"a15ce384-0af7-4b1f-9eb9-dc8158c6cd37","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"9a25006b-cc3e-4043-9c34-7de385e5692b","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"b80bd1d6-5402-4285-96e3-838f92a3a79c","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"68ab67c9-e045-410b-bebc-3568543dfc20","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true}],"title":"Reverse Percentages","topicId":"93ebc5ce-877d-4143-9be4-d6d25a97e5d2","topicSidebar":"$L3a","topicSlug":"grade-5-5-1-reverse-percentages","topicTitle":"Reverse Percentages"}]}],"$L3b","$L3c"]}]