// Numbas version: finer_feedback_settings
{"name": "Solving linear equations: two step", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Solving linear equations: two step", "tags": ["algebra", "balancing equations", "Linear equations", "linear equations", "rearranging equations", "solving equations", "Solving equations", "two step equations"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "(c-b)/a", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped 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"", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "random(2..12 except [h])", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..12 except l)", "description": "", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(-12..12 except [0,1,-1])", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(-12..12 except[0,q])", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "random([-13,-11,-7,-5,-3,-2,13,11,7,5,3,2])", "description": "", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "t": {"name": "t", "group": "Ungrouped variables", "definition": "random([13,11,7,5,3,2] except s)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["a", "b", "c", "ans1", "d", "f", "g", "ans2", "h", "j", "k", "ans3", "l", "m", "n", "ans4", "p", "q", "r", "ans5", "s", "t", "u", "ans6"], "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>Given $\\var{a}x+\\var{b}=\\var{c}$, solving for $x$ gives&nbsp;$x=$&nbsp;[[0]].</p>", "stepsPenalty": "1", "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": "<p>Given $\\var{a}x+\\var{b}=\\var{c}$, we can&nbsp;subtract $\\var{b}$ from both sides to get $\\var{a}x$ by itself, and then divide both sides by $\\var{a}$ to get $x$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{a}x+\\var{b}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{c}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{a}x+\\var{b}-\\var{b}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{c}-\\var{b}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{a}x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{c-b}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{a}x}{\\var{a}}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{c-b}}{\\var{a}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{c-b}/{a}}}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"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": "{c-b}/{a}", "maxValue": "{c-b}/{a}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": 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>Given $\\var{d}-\\var{f}y=\\var{g}$, &nbsp;$y=$&nbsp;[[0]].</p>", "stepsPenalty": "1", "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": "<p>Given $\\var{d}-\\var{f}y=\\var{g}$, we can&nbsp;subtract $\\var{d}$ from both sides to get $-\\var{f}y$ by itself, and then divide both sides by $-\\var{f}$ to get $y$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{d}-\\var{f}y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{d}-\\var{f}y-\\var{d}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}-\\var{d}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$-\\var{f}y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g-d}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{-f}y}{\\var{-f}}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{g-d}}{\\var{-f}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{g-d}/{-f}}}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"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": "{d-g}/{f}", "maxValue": "{d-g}/{f}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": 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>Rearrange $\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$ to determine the value of $z$.</p>\n<p>$z=$&nbsp;[[0]]</p>", "stepsPenalty": "1", "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": "<p>Given $\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$, we add $\\var{j}$ to both sides to get $\\displaystyle{\\frac{z}{\\var{h}}}$&nbsp;by itself and then multiply both sides by $\\var{h}$ to get $z$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}+\\var{j}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k}+\\var{j}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{h}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k+j}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{h}}\\times\\var{h}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k+j}\\times \\var{h}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$z$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans3}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"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": "{ans3}", "maxValue": "{ans3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "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>Solve $\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$ for&nbsp;$a$.</p>\n<p>$a=$&nbsp;[[0]]</p>", "stepsPenalty": "1", "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": "<p>Given $\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$, we can&nbsp;multiply&nbsp;both sides by $\\var{m}$ to get $a-\\var{l}$&nbsp;by itself and then add&nbsp;$\\var{l}$ to both sides to get $a$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{n}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}\\times \\var{m}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{n}\\times\\var{m}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$a-\\var{l}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{n*m}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$a-\\var{l}+\\var{l}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{n*m}+\\var{l}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$a$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans4}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"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": "{ans4}", "maxValue": "{ans4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "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>Solve&nbsp;$\\var{p}=\\var{q}(\\var{r}+b)$.</p>\n<p>$b=$&nbsp;[[0]]</p>", "stepsPenalty": "1", "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": "<p>Given $\\var{p}=\\var{q}(\\var{r}+b)$, we can divide&nbsp;both sides by $\\var{q}$ to get $\\var{r}+b$&nbsp;by itself and then subtract&nbsp;$\\var{r}$ from&nbsp;both sides to get $b$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{p}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{q}(\\var{r}+b)$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{p}}{\\var{q}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{q}(\\var{r}+b)}{\\var{q}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{{p}/{q}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{r}+b$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{{p}/{q}}}-\\var{r}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{r}+b-\\var{r}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{{p-r*q}/{q}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$b$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$b$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{p-r*q}/{q}}}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"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": "{p-r*q}/{q}", "maxValue": "{p-r*q}/{q}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": 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>Solve&nbsp;$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}=\\var{u}$.</p>\n<p>$w=$&nbsp;[[0]]</p>", "stepsPenalty": "1", "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": "<p>Given $\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}=\\var{u}$, we can multiply&nbsp;both sides by $\\var{t}$ to get $\\var{s}w$&nbsp;by itself and then divide both sides by&nbsp;$\\var{s}$ to get $w$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{u}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}\\times\\var{t}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{u}\\times\\var{t}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{s}w$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{u*t}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{s}w}{\\var{s}}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{u*t}}{\\var{s}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$w$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{u*t}/{s}}}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"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": "{u*t}/{s}", "maxValue": "{u*t}/{s}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "resources": []}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}