itle":"Solve for the pen cost","content":"Using our first equation, we can solve for $x$ (the cost of one pen) by dividing both sides by $4$:\n\n$$\\begin{aligned} 4x &= 1.20 \\\\ x &= \\frac{1.20}{4} \\\\ x &= 0.30 \\end{aligned}$$\n\nSo, one pen costs **£0.30** (or 30p). This earns you the first mark."},{"type":"text","order":2,"title":"Solve for the pencil cost","content":"Now we substitute $x = 0.30$ into our second equation to find $y$ (the cost of one pencil):\n\n$$\\begin{aligned} 3(0.30) + 5y &= 1.15 \\\\ 0.90 + 5y &= 1.15 \\end{aligned}$$\n\nSubtract $0.90$ from both sides to find the cost of $5$ pencils:\n\n$$\\begin{aligned} 5y &= 1.15 - 0.90 \\\\ 5y &= 0.25 \\end{aligned}$$\n\nNow, divide by $5$ to find the cost of a single pencil:\n\n$$\\begin{aligned} y &= \\frac{0.25}{5} \\\\ y &= 0.05 \\end{aligned}$$\n\nSo, one pencil costs **£0.05** (or 5p). Finding this value earns you the second mark."},{"type":"text","order":3,"title":"Calculate the target cost","content":"We need to work out the cost of **1 pen and 2 pencils**, which is represented by the algebraic expression:\n\n$$\\text{Total Cost} = x + 2y$$\n\nSubstitute our values of $x = 0.30$ and $y = 0.05$ into this expression:\n\n$$\\begin{aligned} \\text{Total Cost} &= 0.30 + 2(0.05) \\\\ &= 0.30 + 0.10 \\\\ &= 0.40 \\end{aligned}$$\n\nIt would cost **£0.40** (or 40p) to buy 1 pen and 2 pencils. This final calculation earns you the third and final mark.","highlights":[{"text":"Work out how much it would cost to buy 1 pen and 2 pencils.","location":"specification"}]}]}],"generatedAt":"2026-06-12T10:12:43.523Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"ee2a013d-5193-4e38-998c-0f9a4763fe3c","revisionId":"b1c2d9da-d260-40e8-bf9d-8a95c85ecfc0","questionNumber":"8","questionType":"LA","specification":"2 calculators cost £10.40\n3 pens cost £3.54\n\nJude wants to buy 30 calculators and 30 pens. He only has £200.","difficulty":1,"difficultyBand":"medium","totalMarks":4,"sourceTitle":"Calculation Problems","calculatorUse":"non_calc","parts":[{"id":"77a0d106-42f8-486f-83ab-616297cfb523","label":"0","content":"Does Jude have enough money to buy 30 calculators and 30 pens? You must show how you get your answer.","markscheme":"- Cost of 30 calculators: $(30 \\div 2) \\times 10.40 = 156$ M1\n- Cost of 30 pens: $(30 \\div 3) \\times 3.54 = 35.40$ M1\n- Total cost: $156 + 35.40 = 191.40$ M1\n- Conclusion: Yes, $191.40 < 200$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Calculates the cost of 30 calculators ($£156$).","code":"M"},{"id":"p2","marks":1,"description":"Calculates the cost of 30 pens ($£35.40$).","code":"M"},{"id":"p3","marks":1,"description":"Calculates the total cost ($£191.40$).","code":"M"},{"id":"p4","marks":1,"description":"Concludes 'Yes' with supporting evidence that $191.40 < 200$.","code":"A"}],"finalAnswers":["Yes"],"generatedAt":"2026-05-05T10:19:59.179Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"scale_each_cost","label":"Scale each cost","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$30 \\div 2 = \\color{@sky}{\\htmlData{anchor=calc_groups}{15}}$"},{"latex":"$$\\color{@sky}{\\htmlData{anchor=calc_cost}{15}} \\times 10.40 = 156$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"calc_groups"},{"color":"sky","style":"text-color","anchor":"calc_cost"}]},"order":0,"title":"Cost the calculators","description":"First find how many groups of two are needed, then multiply by the cost of each group. This earns the first M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$30 \\div 3 = \\color{@orange}{\\htmlData{anchor=pen_groups}{10}}$"},{"latex":"$$\\color{@orange}{\\htmlData{anchor=pen_cost}{10}} \\times 3.54 = 35.40$"}],"highlights":[{"color":"orange","style":"text-color","anchor":"pen_groups"},{"color":"orange","style":"text-color","anchor":"pen_cost"}]},"order":1,"title":"Cost the pens","description":"Firs

Calculation Problems

Question 48

Calculation Problems Questions

Calculation Problems

Question 48

Calculation Problems Questions