{"id":15367,"date":"2021-10-11T23:05:38","date_gmt":"2021-10-11T23:05:38","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/outcome-problem-solving-with-systems\/"},"modified":"2021-11-01T01:30:18","modified_gmt":"2021-11-01T01:30:18","slug":"introduction-to-problem-solving-with-systems","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/introduction-to-problem-solving-with-systems\/","title":{"raw":"Introduction to Problem Solving With Systems","rendered":"Introduction to Problem Solving With Systems"},"content":{"raw":"<h2>What you'll learn to do: Apply the problem solving method to systems of equations.<\/h2>\r\nApplications of mathematics are what drive innovation and lead to new mathematical discoveries. They also apply to a variety of real world situations. In this section, we will explore how systems of linear equations can be used to model mixtures of chemicals, solve the seemingly unsolvable\u00a0when variables have different values, and anticipate the cost and revenue for a business. It is important to be able to interpret solutions to systems because they tell us important things about the system, and an incorrect interpretation can be misleading.\r\n\r\nSpecifically, in this section you\u2019ll learn how to:\r\n<ul>\r\n \t<li>Solve mixture problems<\/li>\r\n \t<li>Solve value problems<\/li>\r\n \t<li>Solve cost and revenue problems<\/li>\r\n<\/ul>\r\n&nbsp;\r\n<h2>Contribute!<\/h2>\r\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\r\n<a style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\" href=\"https:\/\/docs.google.com\/document\/d\/1m4J2vbvgkgLhVXIgb7LadZa6Hj0Ozxs3bnF74LJHrH8\" target=\"_blank\" rel=\"noopener\">Improve this page<\/a><a style=\"margin-left: 16px;\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>","rendered":"<h2>What you&#8217;ll learn to do: Apply the problem solving method to systems of equations.<\/h2>\n<p>Applications of mathematics are what drive innovation and lead to new mathematical discoveries. They also apply to a variety of real world situations. In this section, we will explore how systems of linear equations can be used to model mixtures of chemicals, solve the seemingly unsolvable\u00a0when variables have different values, and anticipate the cost and revenue for a business. It is important to be able to interpret solutions to systems because they tell us important things about the system, and an incorrect interpretation can be misleading.<\/p>\n<p>Specifically, in this section you\u2019ll learn how to:<\/p>\n<ul>\n<li>Solve mixture problems<\/li>\n<li>Solve value problems<\/li>\n<li>Solve cost and revenue problems<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\" href=\"https:\/\/docs.google.com\/document\/d\/1m4J2vbvgkgLhVXIgb7LadZa6Hj0Ozxs3bnF74LJHrH8\" target=\"_blank\" rel=\"noopener\">Improve this page<\/a><a style=\"margin-left: 16px;\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-15367\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Learning Outcomes and Description. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":167848,"menu_order":28,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Learning Outcomes and Description\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"0b22215a478e41e292cc1317adbff940","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-15367","chapter","type-chapter","status-publish","hentry"],"part":13184,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15367","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/167848"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15367\/revisions"}],"predecessor-version":[{"id":16000,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15367\/revisions\/16000"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/13184"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15367\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=15367"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=15367"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=15367"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=15367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}