// Numbas version: finer_feedback_settings
{"name": "Blending Liquids", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Blending Liquids", "tags": [], "metadata": {"description": "<p>Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>We need to solve \\begin{align} v_1+v_2 - \\var{vol} &amp;=0\\\\\\var{conc_1}v_1 +\\var{conc_2}v_2 &amp;=\\var{conc*vol}\\end{align} which can be written as \\begin{align} v_1+v_2 &amp;= \\var{vol}\\quad (1)\\\\ \\var{conc_1}v_1 +\\var{conc_2}v_2 &amp;=\\var{conc*vol}\\quad (2)\\end{align}</p>\n<p>Using the method of elimination to eliminate \\(v_2\\) we multiply equation \\((1)\\) by \\(-\\var{conc_2}\\) to get \\begin{align}-\\var{conc_2}v_1-\\var{conc_2}v_2 &amp;= -\\var{conc_2*vol}\\quad (3)\\\\ \\var{conc_1}v_1 +\\var{conc_2}v_2 &amp;=\\var{conc*vol}\\quad (4)\\end{align}</p>\n<p>Taking \\((3)+(4)\\) we obtain \\[\\var{conc_1-conc_2}v_1=\\var{(conc-conc_2)*vol}\\]</p>\n<p>and hence \\[v_1=\\var{((conc-conc_2)*vol)/(conc_1-conc_2)}\\]</p>\n<p>Substituting this into \\((1)\\) gives us \\[\\var{((conc-conc_2)*vol)/(conc_1-conc_2)}+v_2 = \\var{conc*vol}\\] and hence \\[v_2=\\var{((conc-conc_2)*vol)/(conc_1-conc_2)}\\]</p>\n<p>Thus the volumes are \\(v_1\\approx\\var{precround(((conc-conc_2)*vol)/(conc_1-conc_2),3)}\\) litres and \\(v_2\\approx\\var{precround(((conc-conc_2)*vol)/(conc_1-conc_2),3)}\\) N.</p>\n<p>(Note that this problem could also be solved by eliminating \\(v_1\\) instead of \\(v_2\\) or by the method of substitution, however the final answers will be the same.)</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"vol": {"name": "vol", "group": "Ungrouped variables", "definition": "random(1..4 #0.5)", "description": "<p>Total volume of solution being blended</p>", "templateType": "anything", "can_override": false}, "conc": {"name": "conc", "group": "Ungrouped variables", "definition": "random(0.12..0.35 #0.01)", "description": "<p>required concentration of final solution</p>", "templateType": "anything", "can_override": false}, "conc_1": {"name": "conc_1", "group": "Ungrouped variables", "definition": "random(0.1..conc*0.75 #0.01)", "description": "<p>concetration of solution 1, set between 0.1 and 0.75*final concentration</p>", "templateType": "anything", "can_override": false}, "conc_2": {"name": "conc_2", "group": "Ungrouped variables", "definition": "random(0.02+conc..2*conc #0.01)", "description": "<p>Concentration of solution 2, set between 0.02+final concentration and 2*final concentration</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["vol", "conc", "conc_1", "conc_2"], "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>An environmental engineer need to blend a single mixture of insecticide spray of volume \\(V=\\var{vol}\\) litres and concentration \\(C=\\var{conc}\\) from two solutions having concentrations \\(c_1=\\var{conc_1}\\) and \\(c_2=\\var{conc_2}\\). If the volumes of each solution are \\(v_1\\) and \\(v_2\\) we have the following system of equations:</p>\n<p>\\begin{align} v_1+v_2-\\var{vol}&amp;=0\\\\\\var{conc_1}v_1+\\var{conc_2}v_2&amp;=\\var{conc*vol}\\end{align}</p>\n<p>Find the volumes \\(v_1\\) and \\(v_2\\) of the solutions required to make up the mixture. Give your answer correct to 3 decimal places and show full working in your handwritten notes.</p>\n<p>\\(v_1=\\)[[0]] litres</p>\n<p>\\(v_2=\\)[[1]] litres</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "\\(v_1\\)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{((conc-conc_2)*vol)/(conc_1-conc_2)}", "maxValue": "{((conc-conc_2)*vol)/(conc_1-conc_2)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "\\(v_2\\)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{((conc-conc_1)*vol)/(conc_2-conc_1)}", "maxValue": "{((conc-conc_1)*vol)/(conc_2-conc_1)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}