// Numbas version: finer_feedback_settings
{"name": "Ratios 2 (NPK)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Ratios 2 (NPK)", "tags": [], "metadata": {"description": "<p>Part (a) - dividing a total quantity given a ratio</p>\n<p>Part (b) - given the value of one part of the ratio to find the total quantity.</p>", "licence": "None specified"}, "statement": "<p>The N:P:K content listed on fertiliser labels is the ratio of nitrogen, phosphorus and potassium (in that order) for that particular fertiliser blend. For a given bag of fertiliser with an N:P:K ratio of:</p>\n<p style=\"text-align: center;\">$\\var{part1}$ : $\\var{part2}$ : $\\var{part3}$</p>\n<p></p>", "advice": "<p><strong>Part (a)</strong></p>\n<p>Divide the quantity {total}kg into parts according to the ratio</p>\n<p style=\"text-align: center;\">{part1} : {part2} : {part3}</p>\n<p style=\"text-align: left;\">Step 1: Find the sum of the parts:</p>\n<p style=\"text-align: left; padding-left: 40px;\">{part1} + {part2} + {part3} = {part1+part2+part3}</p>\n<p style=\"text-align: left;\">Step 2: Divide the total quantity by the sum of the parts to find the value of one part.</p>\n<p style=\"text-align: left; padding-left: 40px;\">$\\frac{\\var{total}}{\\var{s_parts}}$ = {total/(part1+part2+part3)} kg</p>\n<p style=\"text-align: left;\">Step 3: Multiply the value of one part by the number of parts for each nutrient (N, P and K)</p>\n<p style=\"text-align: left; padding-left: 40px;\">N:&nbsp; {total/(part1+part2+part3)} $\\times$ {part1}&nbsp; = <strong>{N_ans_r} kg</strong></p>\n<p style=\"text-align: left; padding-left: 40px;\">P:&nbsp; {total/(part1+part2+part3)} $\\times$ {part2}&nbsp; = <strong>{P_ans_r} kg</strong></p>\n<p style=\"text-align: left; padding-left: 40px;\">K:&nbsp; {total/(part1+part2+part3)} $\\times$ {part3}&nbsp; = <strong>{K_ans_r} kg</strong></p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"><strong>Part (b)</strong></p>\n<p style=\"text-align: left;\">Give the size of one part ({nitrogen} g of nitrogen), find the total mass of the nutrients in the fertiliser.</p>\n<p style=\"text-align: left;\">Step 1: Divide the mass of nitrogen by its number of parts to find the value of one part.</p>\n<p style=\"text-align: left; padding-left: 40px;\">$\\frac{\\var{nitrogen}}{\\var{part1}}$ = {unit_g} g</p>\n<p style=\"text-align: left;\">Step 2: Mutiply the value of one part by the sum of the parts to find the total mass of nutrients.</p>\n<p style=\"text-align: left; padding-left: 40px;\">{unit_g} $\\times$ {s_parts} = <strong>{total_g} g</strong></p>\n<p style=\"text-align: left;\"></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"part1": {"name": "part1", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "part2": {"name": "part2", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "part3": {"name": "part3", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "1 .. 10#1", "description": "", "templateType": "range", "can_override": false}, "total": {"name": "total", "group": "Ungrouped variables", "definition": "random(1..10#0.01 except n)", "description": "", "templateType": "anything", "can_override": false}, "nitrogen": {"name": "nitrogen", "group": "Ungrouped variables", "definition": "random(100..200)", "description": "", "templateType": "anything", "can_override": false}, "N_ans_r": {"name": "N_ans_r", "group": "Ungrouped variables", "definition": "dpformat(total/(part1+part2+part3)*part1,1)", "description": "", "templateType": "anything", "can_override": false}, "P_ans_r": {"name": "P_ans_r", "group": "Ungrouped variables", "definition": "dpformat(total/(part1+part2+part3)*part2,1)", "description": "", "templateType": "anything", "can_override": false}, "K_ans_r": {"name": "K_ans_r", "group": "Ungrouped variables", "definition": "dpformat(total/(part1+part2+part3)*part3,1)", "description": "", "templateType": "anything", "can_override": false}, "s_parts": {"name": "s_parts", "group": "Ungrouped variables", "definition": "part1+part2+part3", "description": "", "templateType": "anything", "can_override": false}, "unit_g": {"name": "unit_g", "group": "Ungrouped variables", "definition": "dpformat(nitrogen/s_parts,4)", "description": "", "templateType": "anything", "can_override": false}, "total_g": {"name": "total_g", "group": "Ungrouped variables", "definition": "dpformat(nitrogen/part1*(part1+part2+part3),0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["part1", "part2", "part3", "n", "total", "nitrogen", "N_ans_r", "P_ans_r", "K_ans_r", "s_parts", "unit_g", "total_g"], "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>If the bag contains $\\var{total}$ kg of this nutrient mix, how many kilograms of each nutrient is present? Express your answer to one decimal place.</p>\n<p>N = [[0]] kg</p>\n<p>P = [[1]] kg</p>\n<p>K = [[2]] kg</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{total/(part1+part2+part3)*part1}", "maxValue": "{total/(part1+part2+part3)*part1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "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": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{total/(part1+part2+part3)*part2}", "maxValue": "{total/(part1+part2+part3)*part2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "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": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{total/(part1+part2+part3)*part3}", "maxValue": "{total/(part1+part2+part3)*part3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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>If a second bag contains $\\var{nitrogen}$ g of nitrogen, what is the total mass of nutrients (N:P:K) in the fertiliser? Express your answer to the nearest whole number.</p>\n<p>Total mass = [[0]] g</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{nitrogen/part1*(part1+part2+part3)}", "maxValue": "{nitrogen/part1*(part1+part2+part3)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "50", "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", "contributors": [{"name": "Katie Bullen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2255/"}], "resources": []}]}], "contributors": [{"name": "Katie Bullen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2255/"}]}