// Numbas version: exam_results_page_options
{"name": "Rearranging equations  to find the value of unknown variable", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Rearranging equations  to find the value of unknown variable", "tags": [], "metadata": {"description": "<p>This exercise will help you rearrange a linear equation to find the value of a given variable</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Solve the following equations for $y$.&nbsp;Enter your answers as fractions, such as 2/3, or integers <strong>but</strong>&nbsp;<strong>not decimals.</strong></p>", "advice": "<p>Use the following steps in both parts to solve for unknown:</p>\n<p>Part a)</p>\n<p>1. Bring the terms of given variable to one side by changing signs.</p>\n<p>Ex- &nbsp;$\\var{a}y - \\var{c}y$ = &nbsp;$\\var{h}y$</p>\n<p>2. Take all the constants to one side by changing signs</p>\n<p>Ex- $\\var{b}- \\var{d}$ = &nbsp;$\\var{w}$</p>\n<p>3. Solving for y, we get-</p>\n<p>$\\ y $= &nbsp;$\\frac {\\var{w}}{\\var{h}}$</p>\n<p></p>\n<p>Part b)</p>\n<p>1. Bring the terms of fractions of variables &nbsp;to one side by changing signs.</p>\n<p>Ex- &nbsp;$\\frac{\\var{m}}{{y}} - \\frac{\\var{s}}{{y}}&nbsp;= &nbsp;\\frac{\\var{o}}{{y}}$</p>\n<p>2. Take all the constants to one side by changing signs</p>\n<p>Ex- $\\var{t}- \\var{n}$ = &nbsp;$\\var{u}$</p>\n<p>3. Solving for y, we get-</p>\n<p>$\\ y $= &nbsp;$(\\frac {\\var{o}}{\\var{u}})$</p>\n<p></p>\n<p>For futther help, check this video-&nbsp;</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<iframe width=\"500\" height=\"375\" src=\"//www.youtube.com/embed/GmMX3-nTWbE\"></iframe></p>", "rulesets": {"std": ["all"]}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"k": {"name": "k", "group": "Ungrouped variables", "definition": "random(4..10)", "description": "", "templateType": "anything", "can_override": false}, "t": {"name": "t", "group": "Ungrouped variables", "definition": "random(2..12 except n)", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "(a-c)", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "b/a", "description": "", "templateType": "anything", "can_override": false}, "z": {"name": "z", "group": "Ungrouped variables", "definition": "precround((m-s)/(t-n),3)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2..4 except a)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(5..8)", "description": "", "templateType": "anything", "can_override": false}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "(t-n)", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "b/(a-c)", "description": "", "templateType": "anything", "can_override": false}, "o": {"name": "o", "group": "Ungrouped variables", "definition": "(m-s)", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "(b+c)/a", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "precround((b-d)/(a-c),3)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "(b-d)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(10..18)", "description": "", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "random(3..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "k", "j", "m", "n", "q", "p", "s", "t", "z", "h", "w", "o", "u"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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>$\\var{a}y + \\var{d}&nbsp;=&nbsp;\\var{b} +\\var{c}y$</p>\n<p>$y=\\;$[[0]]</p>\n<p></p>", "stepsPenalty": 0, "steps": [{"type": "information", "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": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>\n<hr/>\n<p></p>\n<p>Example: &nbsp;&nbsp;<i>5 x </i>- 6 = 3<i> x</i> - 8</p>\n<p>Subtract 3x from both sides of the equation: 2x - 6 = -8</p>\n<p>Add 6 to both sides of the equation: 2x = -2 or x= -1</p>\n<h4 class=\"media-heading\"></h4>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{b-d}/{a-c}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": "<p>Enter your answer as a fraction or an integer and not a decimal.</p>"}, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}