// Numbas version: exam_results_page_options
{"name": "Q5r Write and simplify an algebraic expression (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Q5r Write and simplify an algebraic expression (10+)", "tags": [], "metadata": {"description": "<p>Used in a LANTITE workshop.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Jack, Sue, Lisa and Ben all collect Pokemon cards.&nbsp;</p>\n<p>Sue has <span data-jme-visible=\"Sue=2\">double</span> <span data-jme-visible=\"Sue=3\">triple</span> the number of cards that Jack has.</p>\n<p>Lisa has {Lisa} more cards than Jack.</p>\n<p>Ben has {Ben} fewer cards than Sue.</p>\n<p>Let the pronumeral&nbsp; $c$&nbsp; represent the number of cards that Jack has.</p>", "advice": "<p>Jack has&nbsp; $c$&nbsp; Pokemon cards.</p>\n<p>Sue has&nbsp;<span data-jme-visible=\"Sue=2\">double</span>&nbsp;<span data-jme-visible=\"Sue=3\">triple</span>&nbsp;the number of cards that Jack has.</p>\n<p>Therefore Sue has&nbsp; <span data-jme-visible=\"Sue=2\">$2$</span> <span data-jme-visible=\"Sue=3\">$3$</span>&nbsp; times&nbsp; $c$&nbsp; cards. This is written as&nbsp; <span data-jme-visible=\"Sue=2\">$2c$</span> <span data-jme-visible=\"Sue=3\">$3c$</span>.</p>\n<p>Lisa has&nbsp; $\\var{Lisa}$&nbsp; more cards than Jack.</p>\n<p>Therefore Lisa has $c+\\var{Lisa}$ cards.</p>\n<p>Ben has&nbsp; $\\var{Ben}$&nbsp; fewer cards than Sue.</p>\n<p>Sue has&nbsp; <span data-jme-visible=\"Sue=2\">$2c$</span>&nbsp;<span data-jme-visible=\"Sue=3\">$3c$</span> cards, so Ben has&nbsp;&nbsp;<span data-jme-visible=\"Sue=2\">$2c-\\var{Ben}$</span>&nbsp;<span data-jme-visible=\"Sue=3\">$3c-\\var{Ben}$</span> &nbsp;cards. Note that this is not written $\\var{Ben}-\\var{Sue}c$.</p>\n<p>The total number of cards that the four people have is given by $c+\\var{Sue}c+(c+\\var{Lisa})+(\\var{Sue}c-\\var{Ben})$</p>\n<p>When we collect like terms, we get <span data-jme-visible=\"Sue=2\">$6c+\\var{const}$</span><span data-jme-visible=\"Sue=3\">$8c+\\var{const}$</span>.</p>\n<p>The simplified algebraic expression for the total number of Pokemon cards that Jack, Sue, Lisa and Ben have is&nbsp; <span data-jme-visible=\"Sue=2\">$6c+\\var{const}$</span><span data-jme-visible=\"Sue=3\">$8c+\\var{const}$</span>.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Sue": {"name": "Sue", "group": "Ungrouped variables", "definition": "random(2 .. 3#1)", "description": "", "templateType": "randrange", "can_override": false}, "Lisa": {"name": "Lisa", "group": "Ungrouped variables", "definition": "random(7 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "Ben": {"name": "Ben", "group": "Ungrouped variables", "definition": "random(4 .. 6#1)", "description": "", "templateType": "randrange", "can_override": false}, "const": {"name": "const", "group": "Ungrouped variables", "definition": "{Lisa}-{Ben}", "description": "", "templateType": "anything", "can_override": false}, "coeff": {"name": "coeff", "group": "Ungrouped variables", "definition": "2*Sue+2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Sue", "Lisa", "Ben", "const", "coeff"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Select the correct algebraic expression for the number of cards that each person has (select one dot on each row).</p>", "minMarks": 0, "maxMarks": "4", "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["Sue", "Lisa", "Ben", "Jack, Sue, Lisa and Ben altogether"], "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0]], "layout": {"type": "all", "expression": ""}, "answers": ["$\\text{ }\\var{Sue}c\\text{ }$", "$\\text{ }c+\\var{Lisa}\\text{ }$", "$\\text{ }\\var{Sue}c-\\var{Ben}\\text{ }$", "$\\text{ }\\var{coeff}c+\\var{const}\\text{ }$", "$\\text{ }c^{\\var{Sue}}\\text{ }$", "$\\text{ }\\var{Lisa}c\\text{ }$", "$\\text{ }\\var{Ben}-\\var{Sue}c\\text{ }$", "$\\text{ }\\var{Ben}-\\var{Lisa}c\\text{ }$", "$\\text{ }c^{\\var{Sue}}+\\var{Lisa-Sue+1}c+\\var{Ben}\\text{ }$"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}