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A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Evidence of subtracting the equations to eliminate $x$, resulting in $5y = -15$.","code":"M"},{"id":"p2","marks":1,"description":"Correct calculation of $y = -3$.","code":"A"},{"id":"p3","marks":1,"description":"Correct substitution and solving for $x = 2$.","code":"A"}],"finalAnswers":["x = 2, y = -3"],"generatedAt":"2026-05-06T14:06:28.786Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"elimination","label":"Elimination","steps":[{"type":"text","order":0,"title":"Choose elimination","content":"The coefficients of $x$ are already equal, so subtracting the equations eliminates $x$ immediately."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\bigl(4x+2y\\bigr)-\\bigl(4x-3y\\bigr)=2-17$"},{"latex":"$$4x+2y-4x+3y=-15$"},{"latex":"$$2y+3y=-15$"},{"latex":"$$5y=-15$"}]},"order":1,"title":"Subtract the equations","description":"Subtract the second equation from the first. Rewriting −(−3y) as +3y avoids a common sign error. Reaching 5y = −15 earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=divide_source}{5y=-15}$"},{"latex":"$$\\htmlData{anchor=divide_result}{\\dfrac{5y}{5}=\\dfrac{-15}{5}}$"},{"latex":"$$y=-3$"}],"connections":[{"to":"divide_result","from":"divide_source","color":"orange","label":"divide both sides by 5"}]},"order":2,"title":"Solve for y","description":"Divide both sides by the coefficient of y. Obtaining y = −3 earns the first A1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$4x+2y=2$"},{"latex":"$$\\htmlData{anchor=substitution}{4x+2(-3)=2}$"},{"latex":"$$\\htmlData{anchor=multiplied}{4x-6=2}$"},{"latex":"$$\\htmlData{anchor=added}{4x=8}$"},{"latex":"$$x=2$"}],"connections":[{"to":"multiplied","from":"substitution","color":"orange","label":"multiply"},{"to":"added","from":"multiplied","color":"purple","label":"add 6"}]},"order":3,"title":"Substitute to find x","description":"Put y = −3 into the first original equation, then solve. Obtaining x = 2 earns the final A1, so the complete solution is x = 2, y = −3."}]}],"generatedAt":"2026-07-19T19:03:20.063Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"0d66d1fc-8fdb-4df4-bc24-e1cb8337b663:elimination","label":"Elimination Method","steps":[{"type":"text","order":0,"title":"Label the equations","content":"To solve these simultaneous equations, let's first label them so we can keep track of our steps easily:\n\n$$\\text{Equation (1): } 4x + 2y = 2$$\n$$\\text{Equation (2): } 4x - 3y = 17$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\\begin{aligned} \\text{Equation (1):} \\quad & \\htmlData{anchor=eq1x}{\\color{@sky}{4x}} + \\htmlData{anchor=eq1y}{\\color{@amber}{2y}} = \\htmlData{anchor=eq1val}{\\color{@purple}{2}} \\\\ \\text{Equation (2):} \\quad & \\htmlData{anchor=eq2x}{\\color{@sky}{4x}} - \\htmlData{anchor=eq2y}{\\color{@amber}{3y}} = \\htmlData{anchor=eq2val}{\\color{@purple}{17}} \\end{aligned}$$"},{"text":"Notice that both equations have the same $4x$ term. We can eliminate $x$ by subtracting Equation (2) from Equation (1):"},{"latex":"$$$(\\color{@sky}{4x} - \\color{@sky}{4x}) + (\\color{@amber}{2y} - (-\\color{@amber}{3y})) = \\color{@purple}{2} - \\color{@purple}{17}$$"},{"latex":"$$$\\htmlData{anchor=elim-y}{\\color{@teal}{5y}} = \\htmlData{anchor=elim-val}{\\color{@teal}{-15}}$$"}],"highlights":[{"color":"sky","style":"box","anchor":"eq1x"},{"color":"sky","style":"box","anchor":"eq2x"},{"color":"teal","style":"text-color","anchor":"elim-y"},{"color":"teal","style":"text-color","anchor":"elim-val"}],"connections":[{"to":"eq2x","from":"eq1x","color":"sky","label":"subtracted","style":"solid"}]},"order":1,"title":"Eliminate the $x$ terms","description":"Subtracting Equation (2) from Equation (1) eliminates the $x$ terms because $4x - 4x = 0$."},{"type":"text","order":2,"title":"Solve for $y$","content":"Now, solve the simplified equation for $y$ by dividing both sides by $5$:\n\n$$\\begin{aligned} 5y &= -15 \\\\ y &= \\frac{-15}{5} \\\\ y &= -3 \\end{aligned}$$\n\n*This earns you the first two marks in the markscheme:* \n* **M1** for subtracting the equations to find $5y = -15$\n* **A1** for finding the correct value $y = -3$"},{"type":"hyper_latex","block":{"nodes":[{"text":"Substitute our value of $\\color{@teal}{y = -3}$ back into Equation (1):"},{"latex":"$$$4x + 2(\\htmlData{anchor=sub-y}{\\color{@teal}{-3}}) = 2$$"},{"latex":"$$$\\htmlData{anchor=simplify-eq}{4x - 6} = 2$$"}],"highlights":[{"color":"teal","style":"box","anchor":"sub-y"}],"connections":[{"to":"simplify-eq","from":"sub-y","color":"teal","label":"multiply by 2","style":"dashed"}]},"order":3,"title":"Substitute $y$ to find $x$","description":"Using Equation (1) allows us to determine the value of $x$ by isolating it."},{"type":"text","order":4,"title":"Solve for $x$","content":"Isolate $x$ by adding $6$ to both sides of the equation, then dividing by $4$:\n\n$$\\begin{aligned} 4x - 6 &= 2 \\\\ 4x &= 2 + 6 \\\\ 4x &= 8 \\\\ x &= \\frac{8}{4} \\\\ x &= 2 \\end{aligned}$$\n\n*This earns you the final mark:* \n* **A1** for finding the correct value $x = 2$"},{"type":"text","order":5,"title":"State the final answer","content":"The solution to the simultaneous equations is:\n\n$$x = 2, \\quad y = -3$$ \n\nWe can easily verify this by substituting both values into Equation (2):\n$$4(2) - 3(-3) = 8 + 9 = 17$$\nSince this matches the right-hand side of Equation (2), our solution is correct!"}]},{"id":"0d66d1fc-8fdb-4df4-bc24-e1cb8337b663:substitution","label":"Substitution Method","steps":[{"type":"text","order":0,"title":"Identify the equations","content":"We have a pair of simultaneous equations:\n\n1) $$4x + 2y = 2$$\n2) $$4x - 3y = 17$$\n\nTo solve these using the **Substitution Method**, we want to rearrange one equation to express one term or variable in terms of another, and then substitute it into the second equation."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$4x + 2y = 2$"},{"latex":"$$\text{Subtract } 2y \text{ from both sides:}$"},{"latex":"$$\framebox{\\htmlData{anchor=sub-term}{\\color{@sky}{4x}}} = \\htmlData{anchor=sub-val}{\\color{@sky}{2 - 2y}}$"}],"highlights":[{"color":"sky","style":"box","anchor":"sub-term"},{"color":"sky","style":"text-color","anchor":"sub-val"}],"connections":[]},"order":1,"title":"Rearrange for substitution","description":"Notice that both equations have a $4x$ term. It is easiest to express $4x$ in terms of $y$ using the first equation, rather than isolating a single $x$ or $y$ which would introduce fractions!"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$4x - 3y = 17$"},{"latex":"$$\text{Substitute } \\htmlData{anchor=sub-val-2}{\\color{@sky}{2 - 2y}} \text{ for } \\htmlData{anchor=sub-term-2}{\\color{@sky}{4x}}:$"},{"latex":"$$(\\color{@sky}{2 - 2y}) - 3y = 17$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"sub-val-2"},{"color":"sky","style":"box","anchor":"sub-term-2"}],"connections":[{"to":"sub-term-2","from":"sub-val-2","color":"sky","label":"substitute","style":"dashed"}]},"order":2,"title":"Substitute into equation 2","description":"Now, we replace the $4x$ in the second equation with our expression $(2 - 2y)$."},{"type":"text","order":3,"title":"Solve for y","content":"Now we simplify and solve the resulting single-variable equation:\n\n$$\\begin{aligned}\n2 - 2y - 3y &= 17 \\\\\n2 - 5y &= 17\n\\end{aligned}$$\n\nSubtract $2$ from both sides:\n\n$$-5y = 15$$\n\nDivide by $-5$ to find $y$:\n\n$$y = -3$$\n\nThis earns the first two marks from the markscheme: one method mark for eliminating a variable and one accuracy mark for finding $y = -3$."},{"type":"text","order":4,"title":"Solve for x","content":"Now substitute $y = -3$ back into our expression for $4x$ to find the value of $x$:\n\n$$\\begin{aligned}\n4x &= 2 - 2y \\\\\n4x &= 2 - 2(-3) \\\\\n4x &= 2 + 6 \\\\\n4x &= 8\n\\end{aligned}$$\n\nDivide by $4$:\n\n$$x = 2$$\n\nThis completes the final accuracy mark."},{"type":"text","order":5,"title":"Final verification","content":"We can check our values $x = 2$ and $y = -3$ in the second equation:\n\n$$4(2) - 3(-3) = 8 + 9 = 17$$\n\nSince this is correct, our final solutions are:\n\n$$\\begin{aligned}\nx &= 2 \\\\\ny &= -3\n\\end{aligned}$$\n\n**Final Answer:** $x = 2$, $y = -3$"}]},{"id":"0d66d1fc-8fdb-4df4-bc24-e1cb8337b663:equating_terms","label":"Equating Terms","steps":[{"type":"text","order":0,"title":"Express $4x$ in equation 1","content":"Let's look at the first equation:\n\n$$4x + 2y = 2$$\n\nTo isolate the common term $4x$, we subtract $2y$ from both sides of the equation:\n\n$$4x = 2 - 2y$$","highlights":[{"text":"4x + 2y = 2","location":"specification"}]},{"type":"text","order":1,"title":"Express $4x$ in equation 2","content":"Next, let's look at the second equation:\n\n$$4x - 3y = 17$$\n\nTo isolate $4x$ here, we add $3y$ to both sides:\n\n$$4x = 17 + 3y$$","highlights":[{"text":"4x - 3y = 17","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$4x = \\htmlData{anchor=expr1}{\\color{@sky}{2 - 2y}}$$"},{"latex":"$$$4x = \\htmlData{anchor=expr2}{\\color{@amber}{17 + 3y}}$$"},{"latex":"$$$\\htmlData{anchor=eq1}{\\color{@sky}{2 - 2y}} = \\htmlData{anchor=eq2}{\\color{@amber}{17 + 3y}}$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"expr1"},{"color":"amber","style":"text-color","anchor":"expr2"}],"connections":[{"to":"eq1","from":"expr1","color":"sky","label":"equate","style":"solid"},{"to":"eq2","from":"expr2","color":"amber","label":"equate","style":"solid"}]},"order":2,"title":"Equate the two expressions","description":"Since both expressions are equal to $4x$, we can set them equal to each other."},{"type":"text","order":3,"title":"Solve for $y$","content":"Now we solve the equation for $y$:\n\n$$2 - 2y = 17 + 3y$$\n\nFirst, add $2y$ to both sides to group the $y$ terms together:\n\n$$2 = 17 + 5y$$\n\nNext, subtract $17$ from both sides:\n\n$$-15 = 5y$$\n\nFinally, divide by $5$:\n\n$$y = -3$$\n\n*(This earns you **1 mark** for the method of eliminating a variable and **1 mark** for finding the correct value of $y$.)*"},{"type":"text","order":4,"title":"Substitute to find $x$","content":"Now substitute $y = -3$ back into one of our expressions for $4x$ to find $x$. Let's use the first one:\n\n$$\\begin{aligned} 4x &= 2 - 2y \\\\ 4x &= 2 - 2(-3) \\\\ 4x &= 2 + 6 \\\\ 4x &= 8 \\end{aligned}$$\n\nDivide both sides by $4$:\n\n$$x = 2$$\n\n*(This earns you the final **1 mark**.)*"},{"type":"text","order":5,"title":"State the final solution","content":"The solution to the simultaneous equations is:\n\n$$x = 2, \\quad y = -3$$"}]}],"generatedAt":"2026-06-13T02:02:24.777Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"bde5bcf5-376b-4e7f-aa26-5963aa9f555b","revisionId":"42b4c014-779f-4ddd-9be7-43fec9862977","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","tier":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"da175ff5-4895-47da-9134-dd823a9d79bf","label":"a","content":"A metal workshop produces circular plates and square plates.\nA stack of 5 circular plates and 3 square plates has a total mass of $145\\text{ g}$.\nA stack of 3 circular plates and 4 square plates has a total mass of $131\\text{ g}$.\nWork out the mass of each circular plate and each square plate.","markscheme":"- Sets up equations $5c + 3s = 145$ and $3c + 4s = 131$ M1\n- Multiplies to equate coefficients (e.g., $20c + 12s = 580$ and $9c + 12s = 393$) and subtracts to find $11c = 187$, so $c = 17$ A1\n- Substitutes $c=17$ to find $s = 20$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Sets up two linear simultaneous equations based on the problem context.","code":"M"},{"id":"p2","marks":1,"description":"Correctly eliminates one variable and solves for the first variable (e.g., circular plate = 17).","code":"A"},{"id":"p3","marks":1,"description":"Correctly finds the value of the second variable (e.g., square plate = 20).","code":"A"}],"finalAnswers":["Circular plate: 17, Square plate: 20"],"generatedAt":"2026-05-06T14:06:26.531Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"elimination","label":"Elimination","steps":[{"type":"text","order":0,"title":"Define the variables","content":"Let $c$ be the mass of one circular plate in grams and $s$ be the mass of one square plate in grams."},{"type":"text","order":1,"title":"Form the equations","content":"Translate each stack into an equation:\n\n$$5c+3s=145$$\n\n$$3c+4s=131$$\n\nWriting both correct equations earns **M1**.","highlights":[{"text":"A stack of 5 circular plates and 3 square plates has a total mass of $145\\text{ g}$.","location":"specification"},{"text":"A stack of 3 circular plates and 4 square plates has a total mass of $131\\text{ g}$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$5c+3s=145$"},{"latex":"$$20c+12s=580$"},{"latex":"$$3c+4s=131$"},{"latex":"$$9c+12s=393$"}]},"order":2,"title":"Match the coefficients","description":"Make the coefficients of s equal. Multiply the first equation by 4 and the second equation by 3."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$20c+12s=580$"},{"latex":"$$-9c-12s=-393$"},{"latex":"$$11c=187$"},{"latex":"$$c=17$"}]},"order":3,"title":"Eliminate the squares","description":"Subtract the second scaled equation from the first. The 12s terms cancel. Reaching c = 17 earns the first accuracy mark, A1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$5c+3s=145$"},{"latex":"$$5(17)+3s=145$"},{"latex":"$$85+3s=145$"},{"latex":"$$3s=60$"},{"latex":"$$s=20$"},{"text":"Therefore, the circular plate has mass 17 g and the square plate has mass 20 g."}]},"order":4,"title":"Find the square mass","description":"Substitute c = 17 into the first original equation and solve for s. Obtaining s = 20 earns the final accuracy mark, A1."}]}],"generatedAt":"2026-07-19T15:21:37.110Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"da175ff5-4895-47da-9134-dd823a9d79bf:elimination","label":"Elimination Method","steps":[{"type":"text","order":0,"title":"Define the variables","content":"To start solving, let's define variables for the quantities we are looking for:\n\n* Let $c$ be the mass of one circular plate in grams ($\\text{g}$).\n* Let $s$ be the mass of one square plate in grams ($\\text{g}$).\n\nThis will allow us to translate the word problem into mathematical equations."},{"type":"text","order":1,"title":"Formulate the equations","content":"Using the information given in the problem, we can write down two simultaneous equations:\n\n1. From \"5 circular plates and 3 square plates have a total mass of $145\\text{ g}$\":\n $$5c + 3s = 145 \\quad \\text{--- (Equation 1)}$$\n\n2. From \"3 circular plates and 4 square plates have a total mass of $131\\text{ g}$\":\n $$3c + 4s = 131 \\quad \\text{--- (Equation 2)}$$\n\nFormulating these equations correctly earns you the first mark ($M1$).","highlights":[{"text":"5 circular plates and 3 square plates has a total mass of 145 g","location":"specification"},{"text":"3 circular plates and 4 square plates has a total mass of 131 g","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"text":"We want to eliminate one of the variables by making their coefficients equal. Let's align the coefficients of $s$ by finding the lowest common multiple of 3 and 4, which is 12."},{"latex":"$$$4 \\times (5c + \\htmlData{anchor=s1}{\\color{@sky}{3s}}) = 4 \\times 145 \\implies 20c + \\htmlData{anchor=s1-aligned}{\\color{@sky}{12s}} = 580 \\quad \\text{--- (Equation 3)}$$"},{"latex":"$$$3 \\times (3c + \\htmlData{anchor=s2}{\\color{@sky}{4s}}) = 3 \\times 131 \\implies 9c + \\htmlData{anchor=s2-aligned}{\\color{@sky}{12s}} = 393 \\quad \\text{--- (Equation 4)}$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"s1"},{"color":"sky","style":"text-color","anchor":"s2"}],"connections":[{"to":"s1-aligned","from":"s1","color":"sky","label":"multiply by 4","style":"solid"},{"to":"s2-aligned","from":"s2","color":"sky","label":"multiply by 3","style":"solid"}]},"order":2,"title":"Align the coefficients","description":"Multiply Equation 1 by 4 and Equation 2 by 3 so that both equations have $12s$."},{"type":"text","order":3,"title":"Eliminate to find c","content":"Now, subtract Equation 4 from Equation 3 to eliminate $12s$:\n\n$$\\begin{aligned}\n(20c + 12s) - (9c + 12s) &= 580 - 393 \\\\\n11c &= 187\n\\end{aligned}$$\n\nDivide both sides by $11$ to find the mass of a circular plate, $c$:\n\n$$c = \\frac{187}{11} = 17\\text{ g}$$\n\nFinding this value earns you the second mark ($A1$)."},{"type":"text","order":4,"title":"Substitute to find s","content":"Now substitute $c = 17$ back into one of our original equations to find the value of $s$. Let's use Equation 1:\n\n$$\\begin{aligned}\n5(17) + 3s &= 145 \\\\\n85 + 3s &= 145\n\\end{aligned}$$\n\nSubtract $85$ from both sides:\n\n$$3s = 60$$\n\nDivide by $3$:\n\n$$s = 20\\text{ g}$$\n\nThis final step earns you the third mark ($A1$)."},{"type":"text","order":5,"title":"State the final answer","content":"Thus, the masses of the plates are:\n\n* Mass of each circular plate: **$17\\text{ g}$**\n* Mass of each square plate: **$20\\text{ g}$**"}]},{"id":"da175ff5-4895-47da-9134-dd823a9d79bf:substitution","label":"Substitution Method","steps":[{"type":"text","order":0,"title":"Define the variables","content":"Let's start by defining variables to represent the unknown values we need to find:\n\n* Let $c$ be the mass of one circular plate (in grams).\n* Let $s$ be the mass of one square plate (in grams)."},{"type":"text","order":1,"title":"Set up the equations","content":"We can represent the given information with two simultaneous equations:\n\n1. A stack of 5 circular plates and 3 square plates has a total mass of $145\\text{ g}$:\n\n $$5c + 3s = 145 \\quad \\text{--- (Equation 1)}$$\n\n2. A stack of 3 circular plates and 4 square plates has a total mass of $131\\text{ g}$:\n\n $$3c + 4s = 131 \\quad \\text{--- (Equation 2)}$$","highlights":[{"text":"5 circular plates and 3 square plates has a total mass of 145 g","location":"specification"},{"text":"3 circular plates and 4 square plates has a total mass of 131 g","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{From Equation 1: } 5c + \\htmlData{anchor=s-term}{\\color{@sky}{3s}} = 145$"},{"latex":"$$\\htmlData{anchor=move-s}{5c} = 145 - \\htmlData{anchor=sub-s}{\\color{@sky}{3s}}$"},{"latex":"$$\\htmlData{anchor=c-expr}{\\color{@amber}{c}} = \\frac{145 - 3s}{5}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"s-term"},{"color":"sky","style":"text-color","anchor":"sub-s"},{"color":"amber","style":"text-color","anchor":"c-expr"}],"connections":[{"to":"sub-s","from":"s-term","color":"sky","label":"subtract 3s","style":"solid"},{"to":"c-expr","from":"move-s","color":"amber","label":"divide by 5","style":"solid"}]},"order":2,"title":"Rearrange for one variable","description":"To use the substitution method, we rearrange Equation 1 to express $c$ in terms of $s$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Equation 2: } 3\\htmlData{anchor=c-placeholder}{\\color{@amber}{c}} + 4s = 131$"},{"latex":"$$3\\htmlData{anchor=substituted}{\\color{@amber}{\\left(\\frac{145 - 3s}{5}\\right)}} + 4s = 131$"}],"highlights":[{"color":"amber","style":"box","anchor":"c-placeholder"},{"color":"amber","style":"box","anchor":"substituted"}],"connections":[{"to":"substituted","from":"c-placeholder","color":"amber","label":"substitute c","style":"solid"}]},"order":3,"title":"Substitute into other equation","description":"Now, we substitute this expression for $c$ into Equation 2."},{"type":"text","order":4,"title":"Solve for s","content":"Let's solve this equation for $s$ step-by-step:\n\nMultiply every term by $5$ to eliminate the fraction:\n\n$$3(145 - 3s) + 20s = 655$$\n\nExpand the brackets:\n\n$$435 - 9s + 20s = 655$$\n\nCombine the $s$ terms:\n\n$$435 + 11s = 655$$\n\nSubtract $435$ from both sides:\n\n$$11s = 220$$\n\nDivide by $11$:\n\n$$s = 20$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Substitute } \\htmlData{anchor=s-val}{\\color{@sky}{s = 20}} \\text{ back into our expression for } c:$"},{"latex":"$$c = \\frac{145 - 3(\\htmlData{anchor=s-sub}{\\color{@sky}{20}})}{5}$"},{"latex":"$$c = \\frac{145 - 60}{5} = \\frac{85}{5} = \\htmlData{anchor=final-c}{\\color{@amber}{17}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"s-val"},{"color":"sky","style":"box","anchor":"s-sub"},{"color":"amber","style":"text-color","anchor":"final-c"}],"connections":[{"to":"s-sub","from":"s-val","color":"sky","label":"substitute s","style":"solid"}]},"order":5,"title":"Solve for c","description":"Now substitute $s = 20$ back into our expression for $c$ to find its value."},{"type":"text","order":6,"title":"State the final answer","content":"Thus, the mass of each plate is:\n* **Circular plate:** $17\\text{ g}$\n* **Square plate:** $20\\text{ g}$"}]}],"generatedAt":"2026-06-13T04:13:14.803Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null,"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/bde5bcf5-376b-4e7f-aa26-5963aa9f555b.mp4","durationSeconds":120,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/bde5bcf5-376b-4e7f-aa26-5963aa9f555b.jpg"}}],"subjectCode":"gcse_maths__aqa","summaries":[{"id":"4784a91f-3aaf-4224-b542-c30b8917664c","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"0f481bbd-d2a9-4426-ab83-8aaaa1126e8c","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"10aadfb8-2b8b-42ed-b390-5848a8eef994","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"1af28248-5a45-4bfc-a097-25329043798a","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"1cbf0eaa-e7ba-4e89-8d2a-50347b2ad93a","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"1cc89115-c44e-4df6-bcef-e43fdcf94ff2","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"1cee943d-227a-4015-acba-0e7a03638c81","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"2de4b115-5c84-46c4-9dd6-80cf0de69ce9","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"35e11743-3ace-4035-952d-5d4ff09b00eb","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"37cbe479-d148-4b11-8c39-af437ea3172b","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"57c018cd-5a1c-4497-8765-8ebcd154ebd5","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"6050ead0-2547-417c-a1a4-abf975317a65","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"6966a365-81ce-48c3-9db9-2c172138dfb4","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"766d5cc1-3f6f-44c8-91ab-86eeaaf28119","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"76f3d215-5255-4943-a044-f1f4fdf7484e","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"7750d396-7bb1-48d6-a7fd-8103a10ae435","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"8a6f2e02-ef3a-43e4-9da6-1b68d1eda2ff","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"8c2dc0c2-0db3-40b6-a25f-cf60585d1db2","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"9b21acb5-d606-4113-8d0f-17888cb51fca","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"9b48c833-6908-460d-bcdc-5ae020d02201","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"a6d27838-2935-4adf-8f45-f644dc3add20","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"ae0c9fe5-aea4-4ebe-ac5c-1588a295e2a0","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"beb6904b-aec6-408e-9f9d-ac23cf82fec1","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"bfd3366d-acce-44a4-be32-8c147b45cc3a","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"c71335dd-ec26-437c-86ca-a8c8fc40aee8","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"cb5264c5-d7f7-4955-a3bb-7282565ae3e9","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"d9ab9fb2-5e13-49f1-9fc4-8a3445d763e0","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"eba75584-d1ce-4695-82da-f235e8b135cf","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"b51fa17e-3444-4e3f-89aa-2d857beb0e24","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"015ed7c4-ecff-4d56-814f-d9116f443824","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"03162215-50c7-46a5-936d-93b2809763b3","diff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