{"id":567,"date":"2022-04-17T02:16:52","date_gmt":"2022-04-17T02:16:52","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=567"},"modified":"2025-08-12T11:18:19","modified_gmt":"2025-08-12T11:18:19","slug":"w-11solve-equations-word-problems","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/w-11solve-equations-word-problems\/","title":{"rendered":"W.11Solve equations: word problems"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Solve equations: word problems<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>What Are Word Problems?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Word problems describe a real-life situation using words.<\/li>\n\n\n\n<li>We use <strong>equations<\/strong> to represent these situations mathematically and then solve for unknowns.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Steps to Solve Word Problems Using Equations<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Read the problem carefully.<\/strong><\/li>\n\n\n\n<li><strong>Identify the unknown quantity<\/strong> and assign a variable (e.g., xxx).<\/li>\n\n\n\n<li><strong>Translate the words into an equation<\/strong> using the variable.<\/li>\n\n\n\n<li><strong>Simplify and solve<\/strong> the equation step-by-step.<\/li>\n\n\n\n<li><strong>Check your solution<\/strong> by substituting the value back into the problem context.<\/li>\n\n\n\n<li><strong>Write the answer<\/strong> clearly with units.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Key Phrases and Their Mathematical Meanings<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Word Phrase<\/th><th>Mathematical Operation<\/th><\/tr><\/thead><tbody><tr><td>Sum of<\/td><td>Addition (+)<\/td><\/tr><tr><td>Difference between<\/td><td>Subtraction (\u2013)<\/td><\/tr><tr><td>Product of<\/td><td>Multiplication (\u00d7)<\/td><\/tr><tr><td>Quotient of<\/td><td>Division (\u00f7)<\/td><\/tr><tr><td>More than \/ Increased by<\/td><td>Addition (+)<\/td><\/tr><tr><td>Less than \/ Decreased by<\/td><td>Subtraction (\u2013)<\/td><\/tr><tr><td>Twice \/ Double<\/td><td>Multiply by 2<\/td><\/tr><tr><td>Three times \/ Triple<\/td><td>Multiply by 3<\/td><\/tr><tr><td>Equal to \/ Is<\/td><td>Equals (=)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong> Examples<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Example 1:<\/strong><\/h4>\n\n\n\n<p><em>The sum of a number and 7 is 15. Find the number.<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let the number be x<\/li>\n\n\n\n<li>Equation: x+7=15<\/li>\n\n\n\n<li>Solve: x=15\u22127=8<\/li>\n\n\n\n<li><strong>Answer:<\/strong> The number is 8.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Example 2:<\/strong><\/h4>\n\n\n\n<p><em>Five times a number decreased by 3 is 12. Find the number.<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let the number be x.<\/li>\n\n\n\n<li>Equation: 5x\u22123=12<\/li>\n\n\n\n<li>Solve: 5x=12+3=15<\/li>\n\n\n\n<li>x=155=3<\/li>\n\n\n\n<li><strong>Answer:<\/strong> The number is 3.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Example 3:<\/strong><\/h4>\n\n\n\n<p><em>A rectangle has length 3 meters more than twice its width. The perimeter is 36 meters. Find the length and width.<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let width = w meters.<\/li>\n\n\n\n<li>Length = 2w+3 meters.<\/li>\n\n\n\n<li>Perimeter formula: 2(length+width)=36<\/li>\n\n\n\n<li>Equation: 2((2w+3)+w)=36<\/li>\n\n\n\n<li>Simplify: 2(3w+3)=36<\/li>\n\n\n\n<li>6w=30\u2192 w=5 meters<\/li>\n\n\n\n<li>Length: 2(5)+3=13 meters<\/li>\n\n\n\n<li><strong>Answer:<\/strong> Width = 5 m, Length = 13 m.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Tips for Success<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always define the variable clearly.<\/li>\n\n\n\n<li>Translate phrases carefully into mathematical expressions.<\/li>\n\n\n\n<li>Don\u2019t forget units (meters, liters, rupees, etc.) in your final answer.<\/li>\n\n\n\n<li>Check your answer by plugging it back into the problem statement.<\/li>\n\n\n\n<li>Practice regularly to improve translation and solving skills.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Practice Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The difference between a number and 8 is 14. Find the number.<\/li>\n\n\n\n<li>Twice a number increased by 5 is 21. Find the number.<\/li>\n\n\n\n<li>The sum of three consecutive numbers is 51. Find the numbers.<\/li>\n\n\n\n<li>A number divided by 4 and then increased by 7 gives 13. Find the number.<\/li>\n\n\n\n<li>The length of a rectangle is 4 meters more than its width. The perimeter is 28 meters. Find the dimensions.<\/li>\n<\/ul>\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-background has-normal-font-size\" style=\"background-color:#f193d3\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-cd6277c001c2d452c99ece2c778f3849\" style=\"color:#b00012\"><strong>Alexandra can bake 9 biscuits with each scoop of flour. How many scoops of flour does Alexandra need in order to bake 36 biscuits?<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-f3c94736e1264f2088ac95c90f5f35e5\" style=\"color:#b00012\">&#8212;&#8212;&#8212;scoops<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-2aeb5dbe9fc8784b87d7e7a38b3ce83e\">Write an equation that shows how the number of biscuits Alexandra can bake depends on the number of scoops of flour&nbsp;<em>f<\/em>. Then solve.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-5a4becc308cb949bfbffbc214d8acf6a\">36=9 . f<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-ca374e7b50bd0f8a5a56a7a66bd8fdcb\">4=f   divide both sides by 9<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-a35b11f34333f0d6689a138e9b22e893\">To bake 36 biscuits, Alexandra needs 4 scoops of flour.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#9ff894\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-2e6189e23a69272d99f02ba659854e44\" style=\"color:#b00012\"><strong>Camille can grow 5 flowers with every seed packet. How many seed packets does Camille need to have a total of 25 flowers in her garden?<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-05f2ba63fda296a63c5c1ef20c5d3f2a\" style=\"color:#b00012\">&#8212;-seed packets.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-8fe2addf73c534699f06522211294bb9\">Write an equation that shows how the total number of flowers depends on the number of seed packets used&nbsp;<em>s<\/em>. Then solve.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-3d62fd0debccc61940b988845c435e32\">25&nbsp;=&nbsp;5 \u00b7&nbsp;<em>s<\/em><\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-bd446eee341acd5c7059266988715280\">5&nbsp;=&nbsp;<em>s           Divide both sides by 5<\/em><\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-8ef92a61f8f3a839082bb8b456fc2b24\">To have a total of 25 flowers in her garden, Camille needs 5 seed packets.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#8673e6\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-2e6f8615492ab1fe6ad4260c174012fc\" style=\"color:#b00012\"><strong>Jonathan can grow 4 plants with every seed packet. How many seed packets does Jonathan need to have a total of 24 plants in his back garden?<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-3024d3f3734e72afc3fa726769814993\" style=\"color:#b00012\">&#8212;-&nbsp;seed packets.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-b9872526bcb975c4d5696d9031110def\">Write an equation that shows how the total number of plants depends on the number of seed packets used&nbsp;<em>s<\/em>. Then solve.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-f12ea4fa3235591298e3ace549f2129c\">24&nbsp;=&nbsp;4 \u00b7&nbsp;<em>s<\/em><\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-bbd9e334699f5e2bae4438754089d4d1\">6&nbsp;=&nbsp;<em>s         Divide both sides by 4<\/em><\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-1cba954ec3189d847acedd8463a97011\">To have a total of 24 plants in his back garden,Jonathan needs 6 seed packets.<\/p>\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\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\/95851\/474\/825\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-142.png\" alt=\"\" class=\"wp-image-8920\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-142.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-142-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-142-150x150.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\/36264\/091\/340\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-146.png\" alt=\"\" class=\"wp-image-8921\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-146.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-146-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-146-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve equations: word problems What Are Word Problems? Steps to Solve Word Problems Using Equations Key Phrases and Their Mathematical Meanings Word Phrase Mathematical Operation Sum of Addition (+) Difference between Subtraction (\u2013) Product of Multiplication (\u00d7) Quotient of Division (\u00f7) More than \/ Increased by Addition (+) Less than \/ Decreased by Subtraction (\u2013)<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/w-11solve-equations-word-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.11Solve equations: 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-567","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/567","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=567"}],"version-history":[{"count":18,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/567\/revisions"}],"predecessor-version":[{"id":21162,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/567\/revisions\/21162"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}