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There are $54$ girls. $10\\%$ of the students in the club are boys. Work out the total number of students in the club.","markscheme":"- $100\\% - 10\\% = 90\\%$ (the percentage of girls) M1\n- $54 = 90\\%$, so $10\\% = 6$ or $\\frac{54}{0.9}$ M1\n- $54 + 6 = 60$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculate the percentage of the known quantity (100% - 10% = 90%).","code":"M"},{"id":"p2","marks":1,"description":"Method to find 1%, 10%, or the total by dividing the amount by its percentage decimal.","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 60.","code":"A"}],"finalAnswers":["60"],"generatedAt":"2026-05-06T13:59:54.271Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"percentage_parts","label":"Use percentage parts","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\color{@sky}{\\htmlData{anchor=whole}{100\\%}}-\\color{@red}{\\htmlData{anchor=boys}{10\\%}}=\\color{@green}{\\htmlData{anchor=girlspercent}{90\\%}}$"},{"latex":"$$\\htmlData{anchor=girlsnumber}{54\\text{ girls}}=\\color{@green}{\\htmlData{anchor=share}{90\\%\\text{ of the students}}}$"}],"connections":[{"to":"share","from":"girlspercent","color":"green","label":"represents the girls"}]},"order":0,"title":"Find the girls’ percentage","description":"All students make the whole, so subtract the boys’ percentage. This earns the first M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\color{@green}{90\\%}=9\\times\\color{@orange}{10\\%}$"},{"latex":"$$\\color{@orange}{10\\%}=\\dfrac{\\color{@green}{54}}{\\color{@purple}{9}}=\\color{@red}{6\\text{ students}}$"}]},"order":1,"title":"Find ten per cent","description":"Ten per cent is one of the nine equal ten-per-cent parts in ninety per cent. Dividing the girls’ number by nine earns the second M1 mark."},{"type":"text","order":2,"title":"Find the total","content":"The girls and boys together give the whole club. Adding them correctly earns the A1 accuracy mark.\n\n$$54+6=60\\text{ students}$$"}]}],"generatedAt":"2026-07-19T18:23:20.425Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"78d3f260-70de-4614-aa21-af998f184666:percentage_scaling","label":"Percentage Scaling Method","steps":[{"type":"text","order":0,"title":"Find girl percentage","content":"Since the total percentage of students in the club is $100\\%$ and the boys make up $10\\%$, we can find the percentage of girls by subtracting the percentage of boys from the total:\n\n$$\\text{Percentage of girls} = 100\\% - 10\\% = 90\\%$$\n\nSo, the $54$ girls represent $90\\%$ of the total students in the club.\n\n*(This step earns you the first mark, **M1**)*","highlights":[{"text":"54","location":"specification"},{"text":"10%","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=pct-girls}{\\color{@sky}{90\\%}} \\text{ of the total students} = \\htmlData{anchor=num-girls}{\\color{@sky}{54}}$"},{"latex":"$$\\text{Divide both sides by } 9:$"},{"latex":"$$\\htmlData{anchor=pct-ten}{\\color{@amber}{10\\%}} \\text{ of the total students} = \\htmlData{anchor=num-ten}{\\color{@amber}{6}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"pct-girls"},{"color":"sky","style":"text-color","anchor":"num-girls"},{"color":"amber","style":"text-color","anchor":"pct-ten"},{"color":"amber","style":"text-color","anchor":"num-ten"}],"connections":[{"to":"pct-ten","from":"pct-girls","color":"sky","label":"divide by 9","style":"solid"},{"to":"num-ten","from":"num-girls","color":"sky","label":"divide by 9","style":"solid"}]},"order":1,"title":"Scale down to 10%","description":"We can scale this relation down to find what $10\\%$ of the students is. Since we know $90\\%$ is equal to $54$, dividing both values by $9$ gives us the value for $10\\%$.\n\n*(This calculation earns you the second mark, **M1**)*"},{"type":"text","order":2,"title":"Find the 100% total","content":"Now we can find the total number of students ($100\\%$). \n\nWe can find this either by multiplying our $10\\%$ value by $10$:\n\n$$6 \\times 10 = 60$$\n\nOr by simply adding the boys ($10\\%$) and the girls ($90\\%$) together:\n\n$$\\text{Total students} = 54 + 6 = 60$$\n\nThere are **$60$** total students in the club.\n\n*(Finding the final correct total earns you the accuracy mark, **A1**)*"}]},{"id":"78d3f260-70de-4614-aa21-af998f184666:algebraic","label":"Algebraic Equation","steps":[{"type":"text","order":0,"title":"Define the unknown variable","content":"Let's represent the total number of students in the club with a variable, $x$.\n\n$$\\text{Total number of students} = x$$","highlights":[{"text":"total number of students in the club","location":"specification"}]},{"type":"text","order":1,"title":"Determine percentage of girls","content":"We are given that $10\\%$ of the students are boys. Since the club only consists of boys and girls, the remaining percentage must be girls:\n\n$$\\text{Percentage of girls} = 100\\% - 10\\% = 90\\%$$\n\nIn decimal form, $90\\%$ is written as $0.9$.\n\n*(This earns you the first mark **M1**)*","highlights":[{"text":"10% of the students in the club are boys","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"text":"Since we know there are $54$ girls, and girls represent $90\\%$ (or $0.9$) of the total students ($x$), we can set up our algebraic equation:"},{"latex":"$$\\htmlData{anchor=percentage}{\\color{@sky}{0.9}}\\htmlData{anchor=total}{\\color{@purple}{x}} = \\htmlData{anchor=num-girls}{\\color{@pink}{54}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"percentage"},{"color":"purple","style":"text-color","anchor":"total"},{"color":"pink","style":"text-color","anchor":"num-girls"}],"connections":[{"to":"num-girls","from":"percentage","color":"teal","label":"90% of total","style":"solid"}]},"order":2,"title":"Form the algebraic equation","description":"This equation states that 90% of the total number of students is equal to 54."},{"type":"text","order":3,"title":"Solve for the total","content":"To find $x$, divide both sides of the equation by $0.9$:\n\n$$\\begin{aligned} x &= \\frac{54}{0.9} \\\\ x &= \\frac{540}{9} \\\\ x &= 60 \\end{aligned}$$\n\n*(Setting up this division earns you the second mark **M1**, and finding $60$ earns you the final accuracy mark **A1**)*","calculator":[{"gdc":{"expression":"54 / 0.9","instructions":"Type 54 / 0.9 and press EXE or ENTER"},"ti84":{"expression":"54 / 0.9","instructions":"Press [5] [4] [/] [0] [.] [9] [ENTER]"},"desmos":{"expression":"54/0.9","instructions":"Type 54/0.9 into the input bar"},"description":"You can easily verify this division using your calculator."}]},{"type":"text","order":4,"title":"State the final answer","content":"The total number of students in the club is **$60$**."}]},{"id":"78d3f260-70de-4614-aa21-af998f184666:ratio_parts","label":"Ratio Method","steps":[{"type":"text","order":0,"title":"Find the percentage of girls","content":"Since $10\\%$ of the students are boys, the remaining percentage must represent the girls. \n\nWe calculate this as:\n$$100\\% - 10\\% = 90\\%$$\n\nSo, girls make up $90\\%$ of the club's total membership.","highlights":[{"text":"10% of the students in the club are boys","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\\text{Boys} : \\text{Girls}$$"},{"latex":"$$$\\htmlData{anchor=boys-pct}{\\color{@sky}{10\\%}} : \\htmlData{anchor=girls-pct}{\\color{@pink}{90\\%}}$$"},{"latex":"$$$\\htmlData{anchor=boys-ratio}{\\color{@sky}{1}} : \\htmlData{anchor=girls-ratio}{\\color{@pink}{9}}$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"boys-pct"},{"color":"pink","style":"text-color","anchor":"girls-pct"},{"color":"sky","style":"text-color","anchor":"boys-ratio"},{"color":"pink","style":"text-color","anchor":"girls-ratio"}],"connections":[{"to":"boys-ratio","from":"boys-pct","color":"sky","label":"divide by 10","style":"solid"},{"to":"girls-ratio","from":"girls-pct","color":"pink","label":"divide by 10","style":"solid"}]},"order":1,"title":"Write the ratio","description":"We can express the relationship between boys and girls as a ratio. By dividing both parts by $10\\%$, we simplify the ratio to its simplest integer form: $1 : 9$."},{"type":"text","order":2,"title":"Calculate the number of boys","content":"We are told that there are $54$ girls in the club, which corresponds to the $9$ parts of our ratio.\n\nTo find the value of $1$ part (the number of boys), we divide the number of girls by $9$:\n\n$$\\text{Number of boys} = \\frac{54}{9} = 6$$","highlights":[{"text":"There are 54 girls.","location":"specification"}]},{"type":"text","order":3,"title":"Find the total students","content":"Now that we know there are $54$ girls and $6$ boys, we add them together to find the total number of students in the club:\n\n$$\\text{Total students} = 54 \\text{ (girls)} + 6 \\text{ (boys)} = 60$$"}]}],"generatedAt":"2026-06-13T02:06:07.049Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":68},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/review/1d9ce177-98e9-4af8-b04d-fb85f2db8bfd.mp4","durationSeconds":67,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/review/1d9ce177-98e9-4af8-b04d-fb85f2db8bfd.jpg"}},{"id":"fcc7f13d-25fd-4f5e-ab81-c5e6270f99e3","revisionId":"364859c1-c4ed-4969-b621-02fadfaa7f98","questionNumber":null,"questionType":"LA","specification":"","difficultyBand":"hard","tier":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"382f596f-c453-4a25-948d-ef7ec4bdf5e0","label":"a","content":"There are adults and children in a cinema. There are $48$ adults. $25\\%$ of the people at the cinema are children. Work out the percentage of the people at the cinema who are adults.","markscheme":"$$100\\% - 25\\% = 75\\%$ (adults) B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Finds the percentage of people who are adults","code":"B","acceptable":["$$75\\%$","75%"]}],"finalAnswers":["75%"],"generatedAt":"2026-09-22T14:41:58.583Z","modelVersion":"gpt-5.6-sol"},"tableImages":[],"explanation":null,"options":[]},{"id":"3afa8b2d-80c4-4c40-9b82-727cedd7efe0","label":"b","content":"Hence, work out the total number of people at the cinema.","markscheme":"$$48 = 75\\%$, so $25\\% = 16$ M1\n$48 + 16 = 64$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Uses $48$ as $75\\%$ and finds the number of children represented by $25\\%$","code":"M","acceptable":["$$25\\% = 16$","Finds 16 children"]},{"id":"p2","marks":1,"description":"Adds the number of adults and children to find the total","code":"A","acceptable":["$$48 + 16 = 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Percentages

Question 1

Percentages Questions

Percentages

Question 1

Percentages Questions