// Numbas version: finer_feedback_settings
{"name": "39.h Two substitutions with fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "39.h Two substitutions with fractions", "tags": [], "metadata": {"description": "<p>Substituting a values of $x$ and $z$ into $\\frac{ax+bz}{c}$</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>If $\\var{Var1}=\\var{Var1Sub}$ and $\\var{Var2}=\\var{Var2Sub}$, find the value of</p>\n<p>\\[\\simplify[basic]{({Num1}{Var1}+{Num2}{Var2})/{Num3}}.\\]</p>", "advice": "<p>To substitute a variable for a number we just replace the letter in the equation with the number it is equal to. In this case since $\\var{Var1}=\\var{Var1Sub}$ and $\\var{Var2}=\\var{Var2Sub}$ we get</p>\n<p>\\[\\simplify[basic]{({Num1}{Var1}+{Num2}{Var2})/{Num3}}=\\simplify[basic]{({Num1}{Var1Sub}+{Num2}{Var2Sub})/{Num3}}=\\simplify[basic]{({Num1*Var1Sub}+{Num2*Var2Sub})/{Num3}}=\\simplify[basic]{({Num1*Var1Sub+Num2*Var2Sub})/{Num3}}=\\var{(Num1*Var1Sub+Num2*Var2Sub)/Num3}.\\]</p>\n<p></p>\n<p><a href=\"https://sheffield.ac.uk/mash/maths-resources/maths-all#Sub\" target=\"_blank\" rel=\"noopener\">Use this link to find resources to help you revise substitution into a formula</a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Var1": {"name": "Var1", "group": "Ungrouped variables", "definition": "random([\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"])", "description": "", "templateType": "anything", "can_override": false}, "Var1Sub": {"name": "Var1Sub", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "Var2": {"name": "Var2", "group": "Ungrouped variables", "definition": "random([\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"] except Var1)", "description": "", "templateType": "anything", "can_override": false}, "Var2Sub": {"name": "Var2Sub", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Num2": {"name": "Num2", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "Num3": {"name": "Num3", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "Num3|(Num1*Var1Sub+Num2*Var2Sub)/Num3", "maxRuns": "300"}, "ungrouped_variables": ["Var1", "Var1Sub", "Num1", "Var2", "Var2Sub", "Num2", "Num3"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{(Num1*Var1Sub+Num2*Var2Sub)/Num3}", "maxValue": "{(Num1*Var1Sub+Num2*Var2Sub)/Num3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "resources": []}]}], "contributors": [{"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}]}