= 55$.","code":"M"},{"id":"p3","marks":1,"description":"Finds $x = 10$ and calculates Chris's marbles as 25.","code":"A"}],"finalAnswers":["25"],"generatedAt":"2026-05-07T01:49:44.581Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"form_and_solve_equation","label":"Form and solve an equation","steps":[{"type":"text","order":0,"title":"Define the quantities","content":"Let Adam have $x$ marbles. Then Bradley has $2x$ because he has twice Adam's number, and Chris has $2x+5$.\n\nThis definition earns the first **M1** mark.","highlights":[{"text":"Bradley has twice as many marbles as Adam.","location":"specification"},{"text":"Chris has 5 more marbles than Bradley.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=total}{x+2x+2x+5=55}"},{"latex":"\\htmlData{anchor=collect}{5x+5=55}"},{"latex":"\\htmlData{anchor=subtract}{5x=50}"},{"latex":"\\htmlData{anchor=adam}{x=10}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"total"}],"connections":[{"to":"collect","from":"total","color":"sky","label":"collect like terms"},{"to":"subtract","from":"collect","color":"orange","label":"subtract 5"},{"to":"adam","from":"subtract","color":"green","label":"divide by 5"}]},"order":2,"title":"Solve for Adam","description":"The three expressions must total 55. Writing the first line forms the required total equation and earns the second M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{Chris}=\\htmlData{anchor=expr}{2x+5}"},{"latex":"\\text{Chris}=\\htmlData{anchor=substitute}{2(10)}+5"},{"latex":"\\text{Chris}=\\htmlData{anchor=evaluate}{20}+5"},{"latex":"\\text{Chris}=25"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"expr"},{"color":"green","style":"text-color-with-background","anchor":"substitute"},{"color":"green","style":"text-color-with-background","anchor":"evaluate"}],"connections":[{"to":"substitute","from":"expr","color":"sky","label":"substitute x = 10","style":"solid"},{"to":"evaluate","from":"substitute","color":"green","label":"evaluate","style":"solid"}]},"order":3,"title":"Find Chris's number","description":"Put Adam's value into Chris's expression, 2x + 5. Solving Adam's value and finding Chris's total of 25 earns the A1 mark."}]}],"generatedAt":"2026-07-21T04:05:28.357Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":50},"walkthroughVideo":null},{"id":"42df8ae7-4a0b-408e-9ff3-da297d47c6e9","revisionId":"bb2d09dc-8f5a-43b4-a3cb-f70220c56a55","questionNumber":"11","questionType":"LA","specification":"The size of the largest angle in a triangle is three times the size of the smallest angle.\nThe other angle is $35^\\circ$ more than the smallest angle.","difficulty":3,"difficultyBand":"medium","totalMarks":5,"sourceTitle":"Forming and Solving Equations","calculatorUse":null,"isCalculation":true,"parts":[{"id":"891fc0e6-1075-4cd9-aaa9-b305b2719d31","label":"","content":"Work out, in degrees, the size of each angle in the triangle. You must show your working.","markscheme":"- Defines angles: $x, 3x, x + 35$ M1\n- Forms equation: $x + 3x + x + 35 = 180$ M1\n- Simplifies: $5x = 145$ M1\n- Solves for $x$: $x = 29$ A1\n- Finds all angles: $29^\\circ, 64^\\circ, 87^\\circ$ A1","marks":5,"order":0,"markingRubric":{"totalMarks":5,"points":[{"id":"p1","marks":1,"description":"Assigns variables to the three angles (e.g., $x, 3x, x+35$).","code":"M"},{"id":"p2","marks":1,"description":"Forms equation summing to 180.","code":"M"},{"id":"p3","marks":1,"description":"Simplifies equation to $5x = 145$.","code":"M"},{"id":"p4","marks":1,"description":"Finds the value of the smallest angle ($x = 29$).","code":"A"},{"id":"p5","marks":1,"description":"Calculates all three angles: 29, 64, and 87.","code":"A"}],"finalAnswers":["29, 64, 87"],"generatedAt":"2026-05-07T01:49:44.581Z","modelVersion":"gemini-3-flash-pre

Forming and Solving Equations

Question 1

Forming and Solving Equations Questions

Forming and Solving Equations

Question 1

Forming and Solving Equations Questions