// Numbas version: exam_results_page_options
{"name": "Algebra VI:  Rearranging equations  to find the value of unknown variable", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "m", "n", "s", "t", "f", "g", "w", "h", "u", "o"], "name": "Algebra VI:  Rearranging equations  to find the value of unknown variable", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Use the following steps in both parts to solve for unknown:</p>\n<p>Part a)</p>\n<p>1. Bring the terms of given variable to one side by changing signs.</p>\n<p>Ex- &nbsp;$\\var{a}y - \\var{c}y$ = &nbsp;$\\var{h}y$</p>\n<p>2. Take all the constants to one side by changing signs</p>\n<p>Ex- $\\var{b}- \\var{d}$ = &nbsp;$\\var{w}$</p>\n<p>3. Solving for y, we get-</p>\n<p>$\\ y $= &nbsp;$\\var{f}$</p>\n<p></p>\n<p>Part b)</p>\n<p>1. Bring the terms of fractions of variables &nbsp;to one side by changing signs.</p>\n<p>Ex- &nbsp;$\\frac{\\var{m}}{{y}} - \\frac{\\var{s}}{{y}}&nbsp;= &nbsp;\\frac{\\var{o}}{{y}}$</p>\n<p>2. Take all the constants to one side by changing signs</p>\n<p>Ex- $\\var{t}- \\var{n}$ = &nbsp;$\\var{u}$</p>\n<p>3. Solving for y, we get-</p>\n<p>$\\ y $= &nbsp;$\\var{g}$</p>\n<p></p>\n<p>For further help, check this video-&nbsp;</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<iframe width=\"500\" height=\"375\" src=\"//www.youtube.com/embed/GmMX3-nTWbE\"></iframe></p>", "rulesets": {"std": ["all"]}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$\\var{a}y + \\var{d}&nbsp;=&nbsp;\\var{b} +\\var{c}y$</p>\n<p>$y=\\;$[[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To transpose or rearrange an equation you may:</p>\n<ul style=\"text-align: left;\">\n<li>add or subtract the same quantity to or from both sides, or move one term to the other side of equation by changing the sign.</li>\n<li>multiply or divide both sides by the same quantity</li>\n<li>square or square root both sides</li>\n<li>Expand out brackets or simplify using BIDMAS</li>\n</ul>\n<p>Example:&nbsp;if $8y+ 16 =12+ 4y$,</p>\n<p>1. Move all the constant(s) to the right hand&nbsp;side by changing the sign, and move all the $y$ terms to the left hand side by changing the sign,</p>\n<p>Ex-&nbsp;$8y- 4y = 12 - 16&nbsp;$</p>\n<p>2. Simplify both sides</p>\n<p>Ex- $4y = -4$</p>\n<p>3. Divide the coefficient of $y$ on both sides.</p>\n<p>Ex- $y = -1$,&nbsp;<strong><em>thus making&nbsp;$y$ the subject of the equation.</em></strong></p>\n<p><b>&nbsp;</b></p>\n<h4 class=\"media-heading\"></h4>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{b-d}/{a-c}", "strictPrecision": false, "minValue": "{b-d}/{a-c}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>$\\displaystyle \\frac{\\var{m}}{y}+\\var{n}=\\frac{\\var{s}}{y}+\\var{t}$</p>\n<p>$y=\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To transpose or rearrange an equation you may:</p>\n<ul style=\"text-align: left;\">\n<li>add or subtract the same quantity to or from both sides</li>\n<li>multiply or divide both sides by the same quantity</li>\n<li>square or square root both sides</li>\n<li>Expand out brackets or simplify using BIDMAS</li>\n</ul>\n<p>Example:&nbsp;if $\\frac{6}{y} + 7= 11+ \\frac{2}{y}$</p>\n<p>1. 1. Move all the constant(s) to the right hand&nbsp;side by changing the sign, and move all the $y$ terms to the left hand side by changing the sign,</p>\n<p>Ex-&nbsp;$\\frac{6}{y}- \\frac{2}{y}= 11-7$</p>\n<p>2. Simplify the both sides,</p>\n<p>Ex- $\\frac{4}{y}=4$</p>\n<p>3. Multiply boths sides by the denominator $y$,</p>\n<p>Ex- $4={4}{y}$</p>\n<p>4. Devide the both sides by the coefficent of $y$,</p>\n<p>Ex- ${y}=1$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{m-s}/{t-n}", "strictPrecision": false, "minValue": "{m-s}/{t-n}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Rearrange&nbsp;the following equations to solve for $y$ (Enter your answers&nbsp;in two decimal places only)</p>\n<p>For help, please check this video -&nbsp;<a href=\"https://www.youtube.com/watch?v=9PqygqYo0ck\">https://www.youtube.com/watch?v=9PqygqYo0ck</a></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(5..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..4 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(10..18)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "precround((o/u),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "precround((w/h),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "a-c", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "m": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "o": {"definition": "m-s", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "s": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "u": {"definition": "t-n", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(2..12 except n)", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "b-d", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}}, "metadata": {"description": "<p>This exercise will help you rearrange a linear equation to find the value of a given variable</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}]}]}], "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}]}