[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522557-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-522557-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","systems-of-equations-word-problems-kuta-software-infinite-algebra-1-name","Systems of Equations Word Problems - Kuta Software-Infinite Algebra 1 Name","","Systems of Equations Word Problems focusing on solving linear relationships using given sums, differences, and rate or mixture constraints. Problems cover number pairs, digit-sum and reversal conditions, plane wind speed calculations, ticket pricing with multi-day sales, and boat travel in downstream versus upstream current. Additional contexts include field trips with vans and buses holding equal numbers per vehicle, plus fruit fundraiser box pricing, requiring consistent quantities across two independent groups.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/systems-of-equations-word-problems-kuta-software-infinite-algebra-1-name/522557/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/systems-of-equations-word-problems-kuta-software-infinite-algebra-1-name/522557.png","ImageObject",300,407,{"name":42,"@type":43},"Asher","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you solve the first number-pair problem with a given sum and difference?","Question",{"text":63,"@type":64},"Let the two numbers be x and y, use x+y=12 and x-y=4, then solve the resulting system to get x=8 and y=4.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are wind and plane speeds determined in the plane word problem?",{"text":68,"@type":64},"Use the forward trip and return trip speeds expressed as plane speed ± wind speed, then solve the two equations formed from the given average speeds.",{"name":70,"@type":61,"acceptedAnswer":71},"What method applies to the van-and-bus field trip problems?",{"text":72,"@type":64},"Let each van carry v students and each bus carry b students, then use the two schools’ totals to form a system; solve for v and b since every vehicle type has the same student count across that trip.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522557,1791586185,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":123,"preview_page_count":4},687197207639,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Algebra 1 Name   \nSystems of Equations Word Problems Date  Period   \n1) Find the value of two numbers if their sum is 12 and their difference is 4.  \n2) The difference of two numbers is 3. Their sum is 13. Find the numbers.  \n3) Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.  \n4) The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.  \n5) The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?  \n6) A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?  \n7) The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.  \n8) The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?  \n9) Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?  \n10) Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.  \n11) A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?  \nKuta Software-Infinite Algebra 1 Name___________________________________  \nSystems of Equations Word Problems Date________________ Period____  \n1) Find the value of two numbers if their sum is 12 and their difference is 4.  \n4 and 8  \n2) The difference of two numbers is 3. Their sum is 13. Find the numbers.  \n5 and 8  \n3) Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.  \nPlane: 135 km/h, Wind: 23 km/h  \n4) The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.  \nsenior citizen ticket: $8, child ticket: $14  \n5) The sum of the digits of a certain two-digit number is 7. Reversing its digits i","cbCaiuie4CwnDb3t","https://ap.wps.com/l/cbCaiuie4CwnDb3t","pdf",30839,"English","# Systems of Equations Word Problems\n## Number pair and digit-reversal problems\n## Rate and travel problems (plane, boat)\n## Ticket and pricing problems (multi-day sales, fundraiser boxes)\n## Group travel logistics (vans and buses)","[{\"question\":\"How do you solve the first number-pair problem with a given sum and difference?\",\"answer\":\"Let the two numbers be x and y, use x+y=12 and x-y=4, then solve the resulting system to get x=8 and y=4.\"},{\"question\":\"How are wind and plane speeds determined in the plane word problem?\",\"answer\":\"Use the forward trip and return trip speeds expressed as plane speed ± wind speed, then solve the two equations formed from the given average speeds.\"},{\"question\":\"What method applies to the van-and-bus field trip problems?\",\"answer\":\"Let each van carry v students and each bus carry b students, then use the two schools’ totals to form a system; solve for v and b since every vehicle type has the same student count across that trip.\"}]","Systems of Equations Word Problems - Kuta Software-Infinite Algebra 1 Name | PDF",1791425913]