{"id":321,"date":"2022-04-13T09:03:00","date_gmt":"2022-04-13T09:03:00","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=321"},"modified":"2025-08-12T09:58:44","modified_gmt":"2025-08-12T09:58:44","slug":"t-12-write-linear-equations-to-solve-word-problems","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-12-write-linear-equations-to-solve-word-problems\/","title":{"rendered":"T.12 Write linear equations to solve word problems"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Write linear equations to solve word problems<\/strong><\/h2>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color wp-elements-289ea7b7e76adbd13604806419fcd555\" style=\"color:#74008b\">Key notes:<\/h2>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-35b8f9b0d1a1dc1332740ed94495f8e6\" style=\"color:#000060\"><strong>What is a Linear Equation in a Word Problem?<\/strong><\/h3>\n\n\n\n<p>A <strong>linear equation<\/strong> is an equation that models a real-world situation where variables have a power of <strong>1<\/strong>.<br>It can be used to represent relationships between quantities in <strong>word problems<\/strong>.<\/p>\n\n\n\n<p>General form: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>ax+by=c<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">or <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong> y=mx+b<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-8b4245ba7c3e68524747543e3cc5c77a\" style=\"color:#000020\"><strong> Steps to Write a Linear Equation from a Word Problem<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Understand the problem<\/strong> \u2013 Read carefully and identify what is being asked.<\/li>\n\n\n\n<li><strong>Define the variables<\/strong> \u2013 Choose letters for the unknown quantities.<\/li>\n\n\n\n<li><strong>Identify relationships<\/strong> \u2013 Find sentences that show how quantities are related.<\/li>\n\n\n\n<li><strong>Translate to equation<\/strong> \u2013 Use algebraic symbols to represent the relationship.<\/li>\n\n\n\n<li><strong>Solve the equation<\/strong> \u2013 Find the value(s) of the unknown(s).<\/li>\n\n\n\n<li><strong>Interpret the answer<\/strong> \u2013 Write your answer in words.<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udca1 <strong>Think-Check:<\/strong> The equation should match the wording exactly.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-96c8fe54ec0a0f7c675330bf94b579c8\" style=\"color:#000060\"><strong>Worked Examples<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-e1f6cd06073359976e551810a599eabb\" style=\"color:#000060\"><strong>Example 1 \u2013 Cost of items<\/strong><\/h4>\n\n\n\n<p>A notebook costs \u20b920 and a pen costs \u20b910. If you buy 3 notebooks and 2 pens, the total cost is \u20b980. Write a linear equation.<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Let<br>x= price of notebook<br>y = price of pen<\/p>\n\n\n\n<p>But here prices are given, so instead let:<br>x= number of notebooks<br>y= number of pens<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Relation from problem:<br>Cost of notebooks =20x<br>Cost of pens =10y<br>Total cost = \u20b980<\/p>\n\n\n\n<p><strong>Step 3:<\/strong> Write the equation: <\/p>\n\n\n\n<p class=\"has-text-align-center\">20x+10y=80<\/p>\n\n\n\n<p>\u2705 This is the linear equation representing the problem.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-4cf6bc82c4be7e0a9dc36cb4c8fb941a\" style=\"color:#000060\"><strong>Example 2 \u2013 Age problem<\/strong><\/h4>\n\n\n\n<p>Ravi is 5 years older than twice his sister\u2019s age. If Ravi is 19, write and solve the equation for his sister\u2019s age.<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Let s = sister\u2019s age.<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Relation:<br>Ravi\u2019s age = 2s+5<br>Given Ravi\u2019s age = 19.<\/p>\n\n\n\n<p><strong>Step 3:<\/strong> Equation: <\/p>\n\n\n\n<p class=\"has-text-align-center\">2s+5=19<\/p>\n\n\n\n<p><strong>Step 4:<\/strong> Solve:<br>Subtract 5: 2s=14<br>Divide by 2: s=7<\/p>\n\n\n\n<p>\u2705 Sister\u2019s age is <strong>7 years<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-14f9cc03928dd257fe56bfadd06f2ce1\" style=\"color:#000060\"><strong>Example 3 \u2013 Slope-intercept situation<\/strong><\/h4>\n\n\n\n<p>A taxi charges \u20b950 as a fixed fee plus \u20b915 per kilometer. Write the equation for total cost C in terms of kilometers k.<\/p>\n\n\n\n<p>Fixed fee \u2192 b=50<br>Rate per km \u2192 m=15<\/p>\n\n\n\n<p>Equation: <\/p>\n\n\n\n<p class=\"has-text-align-center\">C=15k+50<\/p>\n\n\n\n<p>\u2705 This is in slope-intercept form y=mx+b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-13fee65f8dc3663dd752c91e3859799a\" style=\"color:#000060\"><strong> Common Word Problem Clues for Equations<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Words in problem<\/th><th>Mathematical meaning<\/th><\/tr><\/thead><tbody><tr><td>total, sum, altogether<\/td><td>+<\/td><\/tr><tr><td>difference, less than, decreased by<\/td><td>\u2212<\/td><\/tr><tr><td>product, times, of<\/td><td>\u00d7<\/td><\/tr><tr><td>per, rate, each<\/td><td>multiplication (slope)<\/td><\/tr><tr><td>is, gives, equals<\/td><td>=<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-9b61a92ba663972d6019411aade0c9eb\" style=\"color:#000060\"><strong>Practice Problems<\/strong><\/h3>\n\n\n\n<p>Write a linear equation for each:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>A fruit seller sells apples for \u20b930 each and bananas for \u20b910 each. If he sells <strong>a<\/strong> apples and <strong>b <\/strong>bananas for \u20b9300 total, write the equation.<\/li>\n\n\n\n<li>A phone company charges \u20b9200 per month plus \u20b92 for every minute of calls. Write the equation for total cost<strong> C<\/strong> in terms of minutes<strong> m<\/strong><\/li>\n\n\n\n<li>The length of a rectangle is 3 more than twice its width. Write the equation if the length is 15 cm.<\/li>\n\n\n\n<li>The sum of two numbers is 50. One number is 4 less than twice the other. Write and solve the equation.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#a7ebd3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-foreground-color has-text-color has-link-color has-normal-font-size wp-elements-86d64b20d98ed6f88ec5246c414277c6\"><strong>Monica has already baked 26 pies, and she can bake 4 pies with each additional cup of sugar she buys. With 12 additional cups of sugar, <\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-normal-font-size wp-elements-dc49b46fe1c8014dc3f08fad14e0e062\" style=\"color:#b00012\"><strong>how many total pies can Monica bake? Write and solve an equation to find the answer.<\/strong><\/p>\n\n\n\n<p>____&nbsp;pies<\/p>\n<\/div><\/div>\n\n\n\n<p>Make a chart.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1684235342374_317\" class=\"wp-block-table\"><table><tbody><tr><td>Additional cups of sugar (<em>s<\/em>)<\/td><td>Calculation of number of pies (<em>p<\/em>)<\/td><td>Number of pies (<em>p<\/em>)<\/td><\/tr><tr><td>0<\/td><td>4(0) + 26<\/td><td>26<\/td><\/tr><tr><td>1<\/td><td>4(1) + 26<\/td><td>30<\/td><\/tr><tr><td>2<\/td><td>4(2) + 26<\/td><td>34<\/td><\/tr><tr><td><em>s<\/em><\/td><td>4(<em>s<\/em>) + 26<\/td><td><strong>4<em>s<\/em>&nbsp;+ 26<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Find the pattern:&nbsp;<em>p<\/em>&nbsp;is 4 times&nbsp;<em>s<\/em>, plus 26.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Write this relationship as an equation.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1684235342374_324\" class=\"wp-block-table\"><table><tbody><tr><td><em>p<\/em>&nbsp;is 4 times&nbsp;<em>s<\/em>, plus 26<\/td><\/tr><tr><td>&nbsp;&nbsp;\u2193&nbsp;&nbsp;<\/td><\/tr><tr><td><em>p<\/em>&nbsp;= 4<em>s<\/em>&nbsp;+ 26<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Now plug s = 12 into this equation and solve for p.<\/p>\n\n\n\n<p>p = 4s + 26<\/p>\n\n\n\n<p>p = 4(12) + 26             Plugin s = 12<\/p>\n\n\n\n<p>p = 48 + 26             Simplify<\/p>\n\n\n\n<p>p = 74<\/p>\n\n\n\n<p>With 12 additional cups of sugar, Monica can bake a total of 74 pies.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#a5bced\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-foreground-color has-text-color has-link-color has-normal-font-size wp-elements-f085d4177f5f368b1fd26729629b566a\"><strong>Zane takes 2 quizzes each week. <\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-normal-font-size wp-elements-15d0ba3579660029c0bed894deb3fecd\" style=\"color:#b00012\"><strong>Write an equation that shows the relationship between the number of weeks&nbsp;<em>w<\/em>&nbsp;and the total number of quizzes&nbsp;<em>q<\/em>.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Make a chart.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1684235461296_319\" class=\"wp-block-table\"><table><tbody><tr><td>Number of weeks (<em>w<\/em>)<\/td><td>Calculation of total number of quizzes (<em>q<\/em>)<\/td><td>Total number of quizzes (<em>q<\/em>)<\/td><\/tr><tr><td>1<\/td><td>2(1)<\/td><td>2<\/td><\/tr><tr><td>2<\/td><td>2(2)<\/td><td>4<\/td><\/tr><tr><td>3<\/td><td>2(3)<\/td><td>6<\/td><\/tr><tr><td><em>w<\/em><\/td><td>2(<em>w<\/em>)<\/td><td><strong>2<em>w<\/em><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Find the pattern:&nbsp;<em>q<\/em>&nbsp;is 2 times&nbsp;<em>w<\/em>.<\/p>\n\n\n\n<p>Write this relationship as an equation.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><em>q<\/em>&nbsp;is 2 times&nbsp;<em>w<\/em><\/td><\/tr><tr><td>&nbsp;&nbsp;\u2193&nbsp;&nbsp;<\/td><\/tr><tr><td><em>q<\/em>&nbsp;= 2<em>w<\/em><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#ea9090\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-foreground-color has-text-color has-link-color has-normal-font-size wp-elements-109fdd388ccd2912df9b18aa4510de56\"><strong>Noah has already taken 7 pages of notes on his own, and he will take 2 pages during each hour of class. <\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-normal-font-size wp-elements-53aa083967000ae6a7aa5a03608b2f02\" style=\"color:#b00012\"><strong>Write an equation that shows the relationship between the time in class h and the number of pages p.<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\">Write your answer as an equation with p first, followed by an equals sign._____<\/p>\n<\/div><\/div>\n\n\n\n<p>Make a chart.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Time in class (<em>h<\/em>)<\/td><td>Calculation of number of pages (<em>p<\/em>)<\/td><td>Number of pages (<em>p<\/em>)<\/td><\/tr><tr><td>0<\/td><td>2(0) + 7<\/td><td>7<\/td><\/tr><tr><td>1<\/td><td>2(1) + 7<\/td><td>9<\/td><\/tr><tr><td>2<\/td><td>2(2) + 7<\/td><td>11<\/td><\/tr><tr><td><em>h<\/em><\/td><td>2(<em>h<\/em>) + 7<\/td><td><strong>2<em>h<\/em>&nbsp;+ 7<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Find the pattern:&nbsp;<em>p<\/em>&nbsp;is 2 times&nbsp;<em>h<\/em>, plus 7.<\/p>\n\n\n\n<p>Write this relationship as an equation.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><em>p<\/em>&nbsp;is 2 times&nbsp;<em>h<\/em>, plus 7<\/td><\/tr><tr><td>&nbsp;&nbsp;\u2193&nbsp;&nbsp;<\/td><\/tr><tr><td><em>p<\/em>&nbsp;= 2<em>h<\/em>&nbsp;+ 7<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/78189\/255\/632\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-120.png\" alt=\"\" class=\"wp-image-8060\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-120.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-120-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-120-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/78019\/791\/718\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-129.png\" alt=\"\" class=\"wp-image-8061\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-129.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-129-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-129-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Write linear equations to solve word problems Key notes: What is a Linear Equation in a Word Problem? A linear equation is an equation that models a real-world situation where variables have a power of 1.It can be used to represent relationships between quantities in word problems. General form: ax+by=c or y=mx+b Steps to Write<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-12-write-linear-equations-to-solve-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.12 Write linear equations to solve word problems&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-321","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/321","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=321"}],"version-history":[{"count":21,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/321\/revisions"}],"predecessor-version":[{"id":17407,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/321\/revisions\/17407"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}