[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-637934-105":59,"doc-detail-637934-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","inequalities-from-word-problems-c1-answers","INEQUALITIES FROM WORD PROBLEMS C1 - Answers","","Inequalities from word problems (C1) provides eight worked examples translating real-life constraints into algebraic inequalities. Each problem defines inclusive or exclusive bounds, introduces a variable, sets up proportional or difference relationships, and then derives the inequality range. Topics include perimeter/area fencing constraints, running time for a distance, remaining money after spending a fraction, swimming time scaled by lengths, production rate for models, savings as a percentage of salary, travel time for a remaining distance, and age comparisons using linear inequalities.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/inequalities-from-word-problems-c1-answers/637934/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/inequalities-from-word-problems-c1-answers/637934.png","ImageObject",300,407,{"name":92,"@type":93},"dhado","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-22",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you write an inequality when a range is inclusive (e.g., between 40 and 60 inclusive)?","Question",{"text":112,"@type":113},"Translate the quantities into the variable and use ≤ and ≥ so the endpoints are included. For example, “between 40 and 60 yards inclusive” leads to 10 ≤ s ≤ 15 after scaling by 4.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does “exclusive” mean in these word problems, and how is it shown in the inequality?",{"text":117,"@type":113},"Exclusive bounds exclude the endpoints, so you use \u003C or > instead of ≤ or ≥. For instance, “between 25 to 32 seconds (exclusive)” produces 500 \u003C t \u003C 640 after multiplying by 20.",{"name":119,"@type":110,"acceptedAnswer":120},"How are inequalities formed when the problem includes fractions of money (more than half, but less than three-quarters)?",{"text":121,"@type":113},"Use the given total to convert each fraction into a numeric bound for the remaining amount, then combine them into a strict inequality. Example 3 gives $80 ≤ m \u003C $120.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},637934,1792904458,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24},5909893218464,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Name Date  \nINEQUALITIES FROM WORD PROBLEMS C1  \n| WORD PROBLEM WORKING OUT |  |  |\n| --- | --- | --- |\n| 1) | A farmer has a between 40 and 60 yards of fencing (inclusive) to make a square enclosure.\u003Cbr>If his field has sides length s, write an inequality to show what size field he can make. | |\n| 2) | It takes Alice between 10 and 12 minutes (inclusive) to run a mile.\u003Cbr>At this pace, how long would it take her to run a half marathon (13 miles)?\u003Cbr>Write an inequality using the variable t to show this. | |\n| 3) | Flame goes shopping with $240. She spends more than half but less than three-quarters of the money.\u003Cbr>Write an inequality using the variable m to show how much money she has left over. | |\n| 4) | It takes Newton’s between 25 to 32 seconds (exclusive) to swim a length of a swimming pool\u003Cbr>Write an inequality to show the time it takes (t) in seconds for him to swim 20 lengths. | |\n| 5) | Sally can make from 6 to 10 Fimo models in a day. She needs to make 120 models for an exhibition.\u003Cbr>Write an inequality involving the variable x to show how long it will take her to make all the models. | |\n| 6) | Bert has a salary of $26,000 . He is trying to save between 5% and 10% of his salary each year. He has already saved $500 so far this year.\u003Cbr>Write an inequality using the variable s to show how much more money he needs to save. | |\n| 7) | Captain is driving o a 360 mile journey. His speed is averaging between 45 and 60 miles per hour (inclusive). He has traveled 60 miles so far.\u003Cbr>Write an inequality involving the variable r to show how it will take him to complete the remainder of his journey. | |\n| 8) Bill is 2 years younger than Anna. Chris is more than twice as old, but less than 3 times as old, as Bill. If Alice is 9 years old, write an inequality using the variable c to show how old Chris is. |  | |\n\nName Date  \nINEQUALITIES FROM WORD PROBLEMS C1 ANSWERS  \n| WORD PROBLEM WORKING OUT |  |  |  |  |\n| --- | --- | --- | --- | --- |\n| 1) | A farmer has a between 40 and 60 yards of fencing (inclusive) to make a square enclosure.\u003Cbr>If his field has sides length s, write an inequality to show what size field he can make. | |  | 40 ÷ 4 = 10\u003Cbr>60 ÷ 4 = 15\u003Cbr>10 ≤ s ≤ 15 yards |\n| 2) | It takes Alice between 10 and 12 minutes (inclusive) to run a mile.\u003Cbr>At this pace, how long would it take her to run a half marathon (13 miles)?\u003Cbr>Write an inequality using the variable t to show this. | |  | 10 x 13 = 130\u003Cbr>12 x 13 = 156\u003Cbr>130 ≤ t ≤ 156\u003Cbr>minutes |\n| 3) | Flame goes shopping with $240. She spends more than half but less than three-quarters of the money.\u003Cbr>Write an inequality using the variable m to show how much money she has left over. | |  | ½ of 240 = 120 ⅓ of 240 = 80 $80 ≤ m \u003C $120 |\n| 4) | It takes Newton’s between 25 to 32 seconds (exclusive) to swim a length of a swimming pool\u003Cbr>Write an inequality to show the time it takes (t) in seconds for him to swim 20 lengths. | |  | 20 x 25 = 500\u003Cbr>20 x 32 = 640\u003Cbr>500 \u003C t \u003C 640\u003Cbr>seconds |\n| 5) | Sally can make from 6 to 10 Fimo models in a day. She needs to make 120 models for an exhibition.\u003Cbr>Write an inequality involving the variable x to show how long it will take her to make all the models. | |  | 120 ÷ 6 = 20\u003Cbr>120 ÷ 10 = 12\u003Cbr>12 ≤ x ≤ 20 days |\n| 6) | Bert has a salary of $26,000 . He is trying to save between 5% and 10% of his salary each year. He has already saved $500 so far this year.\u003Cbr>Write an inequality using the variable s to show how much more money he needs to save. | | 10% of 26,000 =2600 5% of 26,000 = 1300 1300 – 500 = 800 2600 – 500 = 2100 $800 ≤ s ≤ $2100 |  |\n| 7) | Captain is driving o a 360 mile journey. His speed is averaging between 45 and 60 miles per hour (inclusive). He has traveled 60 miles so far.\u003Cbr>Write an inequality involving the variable r to show how it will take him to complete the remainder of his journey. | | 360 – 60 = 300 miles\u003Cbr>300 ÷ 45 = 6 ⅔ hours\u003Cbr>6 ⅔ h = 6 h 40 min\u003Cbr>300 ÷ 60 = 5 hours\u003Cbr>5 hours ≤ r ≤ 6 h 40","cbCaivubQx0RDahK","https://ap.wps.com/l/cbCaivubQx0RDahK","pdf",233007,"English","# Word Problem Working Out\n## Questions 1-8\n# Answers\n## Solutions 1-8","[{\"question\":\"How do you write an inequality when a range is inclusive (e.g., between 40 and 60 inclusive)?\",\"answer\":\"Translate the quantities into the variable and use ≤ and ≥ so the endpoints are included. For example, “between 40 and 60 yards inclusive” leads to 10 ≤ s ≤ 15 after scaling by 4.\"},{\"question\":\"What does “exclusive” mean in these word problems, and how is it shown in the inequality?\",\"answer\":\"Exclusive bounds exclude the endpoints, so you use \\u003c or \\u003e instead of ≤ or ≥. For instance, “between 25 to 32 seconds (exclusive)” produces 500 \\u003c t \\u003c 640 after multiplying by 20.\"},{\"question\":\"How are inequalities formed when the problem includes fractions of money (more than half, but less than three-quarters)?\",\"answer\":\"Use the given total to convert each fraction into a numeric bound for the remaining amount, then combine them into a strict inequality. Example 3 gives $80 ≤ m \\u003c $120.\"}]","INEQUALITIES FROM WORD PROBLEMS C1 - Answers | PDF",1792681728]