// Numbas version: exam_results_page_options
{"name": "Manipulation of formula 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Manipulation of&nbsp;algebraic fractions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "tags": [], "extensions": [], "ungrouped_variables": ["a", "b", "c", "d"], "variables": {"c": {"description": "", "definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "c"}, "b": {"description": "", "definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b"}, "a": {"description": "", "definition": "random(6..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a"}, "d": {"description": "", "definition": "random(8..16#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "d"}}, "variable_groups": [], "variablesTest": {"condition": "{a}*{d}>{c}*{b}", "maxRuns": 100}, "rulesets": {}, "name": "Manipulation of formula 2", "parts": [{"type": "gapfill", "prompt": "<p>Express your answer as a fraction:</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;\\(V =\\)&nbsp;[[0]]</p>", "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "gaps": [{"type": "jme", "answer": "((5*{b}-{d})R+8)/(({a}*{d}-{b}*{c})R+7*{a}-3*{c})", "scripts": {}, "showpreview": true, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "showFeedbackIcon": true, "checkvariablenames": false, "showCorrectAnswer": true, "variableReplacements": [], "checkingaccuracy": 0.001, "checkingtype": "absdiff", "vsetrange": [0, 1], "marks": "2"}], "marks": 0, "showFeedbackIcon": true, "variableReplacements": []}], "preamble": {"css": "", "js": ""}, "functions": {}, "advice": "<p>When one fraction equals another fraction we can clear both fractions by cross-multiplying:</p>\n<p style=\"text-align: center;\">\\((\\var{a}V+1)*(\\var{d}R+7)=(\\var{b}R+3)*(\\var{c}V+5)\\)</p>\n<p style=\"text-align: center;\">\\(\\simplify{{a}*{d}}VR+\\simplify{7*{a}}V+\\var{d}R+7=\\simplify{{b}*{c}}VR+\\simplify{5*{b}}R+\\simplify{3*{c}}V+15\\)</p>\n<p>Gathering all the terms involving \\(V\\) to the left hand side and moving all other terms to the right hand side gives</p>\n<p style=\"text-align: center;\">\\(\\simplify{{a}*{d}-{b}*{c}}VR+\\simplify{7*{a}-3*{c}}V=\\simplify{5*{b}-{d}}R+8\\)</p>\n<p>Factoring \\(V\\) out on the left hand side&nbsp;</p>\n<p style=\"text-align: center;\">\\(V(\\simplify{{a}*{d}-{b}*{c}}R+\\simplify{7*{a}-3*{c}})=\\simplify{5*{b}-{d}}R+8\\)</p>\n<p>Thus</p>\n<p style=\"text-align: center;\">\\(V=\\frac{\\simplify{5*{b}-{d}}R+8}{\\simplify{{a}*{d}-{b}*{c}}R+\\simplify{7*{a}-3*{c}}}\\)</p>", "statement": "<p>Rearrange the following expression to make V the subject:</p>\n<p>&nbsp; &nbsp; &nbsp;\\(\\frac{\\var{a}V+1}{\\var{b}R+3}=\\frac{\\var{c}V+5}{\\var{d}R+7}\\)</p>", "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}