// Numbas version: exam_results_page_options
{"name": "Given a formula for something use it (drip rate)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "statement": "<p>Write the following question down on paper and evaluate&nbsp;it without using a calculator.</p>\n<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Show steps</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again.</p>", "variable_groups": [], "ungrouped_variables": ["v", "f", "h", "drip", "driprounded", "cfvh", "v'", "h'", "cfvs", "v''", "s'", "cffh'", "f'", "h''", "cffs'", "f''", "s''", "vf", "hs", "vf''", "hs''"], "parts": [{"prompt": "<p>You are told that&nbsp;&nbsp;</p>\n<p>$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\text{volume (mL)} \\times \\text{drop factor (drops/mL)}}{\\text{time (hr)}\\times \\text{60 (min/hr)}}$</p>\n<p>If the volume is $\\var{v}$ mL,&nbsp;the duration is $\\var{h}$ hours and&nbsp;there are&nbsp;$\\var{f}$ drops/mL, then the drip rate is</p>\n<p>[[0]] (drops/min) to the nearest whole number</p>", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "steps": [{"prompt": "<p>We take the formula</p>\n<p>$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\text{volume (mL)} \\times \\text{drop factor (drops/mL)}}{\\text{time (hr)}\\times \\text{60 (min/hr)}}$</p>\n<p>and substitute the following</p>\n<p>$\\text{volume}=\\var{v}$,</p>\n<p>$\\text{drop factor}= \\var{f}$,</p>\n<p>$\\text{time}= \\var{h}$</p>\n<p>so that we have&nbsp;</p>\n<p>$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v} \\times \\var{f}}{\\var{h}\\times 60}$</p>\n<p>Using a <strong>calculator</strong>&nbsp;we would find</p>\n<p>$\\begin{align}\\text{drip rate (dpm)}&amp;\\approx\\var{drip} \\text{ dpm}\\\\&amp;=\\var{driprounded}\\text{ dpm (to the nearest whole number)}\\end{align}$</p>\n<p></p>\n<p><strong>Without a calculator</strong>, you&nbsp;<strong>could</strong> do this calculation by&nbsp;</p>\n<ul>\n<li>first determining $\\var{v} \\times \\var{f}=\\var{vf}$,</li>\n<li>then $\\var{h}&nbsp;\\times 60=\\var{hs}$,</li>\n<li>and&nbsp;then using long division for&nbsp;&nbsp;$\\displaystyle \\frac{\\var{vf}}{\\var{hs}}&nbsp;=\\var{driprounded}$ <span data-jme-visible=\"drip&lt;&gt;driprounded\">(nearest whole number).</span></li>\n</ul>\n<p>However, it is often best to look for <strong>common factors and cancel</strong> them before the multiplication and division. That is, given:</p>\n<p>$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v} \\times \\var{f}}{\\var{h}\\times 60}$</p>\n<p>I would look for a common factor between $\\var{v}$ and $\\var{h}$.&nbsp;<span data-jme-visible=\"cfvh=1\"> But, alas, there isn't one.</span>&nbsp;<span data-jme-visible=\"cfvh&gt;1\">There is a common factor of&nbsp;$\\var{cfvh}$, so&nbsp;I'd remove this from the top and bottom and be left with</span></p>\n<p><span data-jme-visible=\"cfvh&gt;1\">$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v'} \\times \\var{f}}{\\var{h'}\\times 60}$</span></p>\n<p>Then I'd look for a common factor between $\\var{v'}$ and $\\var{60}$. <span data-jme-visible=\"cfvs=1\"> But, alas, there isn't one.</span> <span data-jme-visible=\"cfvs&gt;1\">There is a common factor of $\\var{cfvs}$, so I'd remove that from the top and bottom and be left with</span></p>\n<p><span data-jme-visible=\"cfvs&gt;1\">$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v''} \\times \\var{f}}{\\var{h'}\\times \\var{s'}}$</span></p>\n<p><span data-jme-visible=\"h'&gt;1\">Then I'd look for a common factor between $\\var{f}$ and $\\var{h'}$.</span> <span data-jme-visible=\"h'&gt;1 and cffh'=1\"> But, alas, there isn't one.</span> <span data-jme-visible=\"h'&gt;1 and cffh'&gt;1\">There is a common factor of $\\var{cffh'}$, so I'd remove that from the top and bottom and be left with</span></p>\n<p><span data-jme-visible=\"h'&gt;1 and cffh'&gt;1\">$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v''} \\times \\var{f'}}{\\var{h''}\\times \\var{s'}}$</span></p>\n<p><span data-jme-visible=\"s'&gt;1\">Then I'd look for a common factor between $\\var{f'}$ and $\\var{s'}$.</span> <span data-jme-visible=\"s'&gt;1 and cffs'=1\"> But, alas, there isn't one.</span> <span data-jme-visible=\"s'&gt;1 and cffs'&gt;1\">There is a common factor of $\\var{cffs'}$, so I'd remove that from the top and the bottom and be left with&nbsp;</span></p>\n<p><span data-jme-visible=\"s'&gt;1 and cffs'&gt;1\">$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v''} \\times \\var{f''}}{\\var{h''}\\times \\var{s''}}$</span></p>\n<p></p>\n<p>So, after all that, I only need to do</p>\n<ul>\n<li>$\\var{v''} \\times \\var{f''}=\\var{vf''}$,</li>\n<li>then $\\var{h''}&nbsp;\\times \\var{s''}=\\var{hs''}$,</li>\n<li>and then perform the&nbsp;division $\\displaystyle \\frac{\\var{v''*f''}}{\\var{s''*h''}}=\\var{driprounded}$ <span data-jme-visible=\"drip&lt;&gt;driprounded\">(nearest whole number)</span></li>\n</ul>", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "customName": "", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "information", "marks": 0, "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": []}], "customName": "", "customMarkingAlgorithm": "", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "gaps": [{"minValue": "drip", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to&nbsp;the nearest whole number.", "useCustomName": false, "variableReplacements": [], "customName": "", "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "marks": 1, "scripts": {}, "unitTests": [], "correctAnswerFraction": false, "allowFractions": false, "showFeedbackIcon": true, "precisionType": "dp", "strictPrecision": false, "precisionPartialCredit": 0, "type": "numberentry", "maxValue": "drip", "precision": 0, "showPrecisionHint": false, "showCorrectAnswer": true}], "variableReplacements": []}], "variables": {"v": {"definition": "random(random(500,1000),random(100..1000#100))", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "v"}, "s'": {"definition": "60/cfvs", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "s'"}, "cffh'": {"definition": "gcd(f,h')", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "cffh'"}, "vf''": {"definition": "v''*f''", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "vf''"}, "driprounded": {"definition": "precround(drip,0)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "driprounded"}, "h": {"definition": "random(2..6)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "h"}, "cffs'": {"definition": "gcd(f',s')", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "cffs'"}, "hs": {"definition": "h*60", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "hs"}, "h'": {"definition": "h/cfvh", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "h'"}, "f'": {"definition": "f/cffh'", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "f'"}, "f''": {"definition": "f'/cffs'", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "f''"}, "v'": {"definition": "v/cfvh", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "v'"}, "v''": {"definition": "v'/cfvs", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "v''"}, "vf": {"definition": "v*f", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "vf"}, "cfvh": {"definition": "gcd(v,h)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "cfvh"}, "hs''": {"definition": "h''*s''", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "hs''"}, "cfvs": {"definition": "gcd(v',60)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "cfvs"}, "drip": {"definition": "(v*f)/(h*60)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "drip"}, "h''": {"definition": "h'/cffh'", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "h''"}, "s''": {"definition": "s'/cffs'", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "s''"}, "f": {"definition": "random(20,60)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "f"}}, "preamble": {"css": "", "js": ""}, "name": "Given a formula for something use it (drip rate)", "functions": {}, "metadata": {"description": "Checking if a student can substitute into an equation. This is a nursing calculation question. Solution is given for with a calculator and without a calculator, however the point of this question is really substitution.&nbsp;&nbsp;", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "advice": "", "rulesets": {}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}