{"id":9350,"date":"2017-05-02T21:46:57","date_gmt":"2017-05-02T21:46:57","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9350"},"modified":"2017-09-23T19:07:35","modified_gmt":"2017-09-23T19:07:35","slug":"applications-with-adding-integers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/applications-with-adding-integers\/","title":{"raw":"Applications With Adding Integers","rendered":"Applications With Adding Integers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate word phrases to algebraic expressions<\/li>\r\n \t<li>Simplify algebraic expressions using the order of operations<\/li>\r\n \t<li>Add integers in application problems<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Translate Word Phrases to Algebraic Expressions<\/h3>\r\nAll our earlier work translating word phrases to algebra also applies to expressions that include both positive and negative numbers. Remember that the phrase <em>the sum<\/em> indicates addition.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and simplify: the sum of [latex]-9[\/latex] and [latex]5[\/latex].\r\n\r\nSolution:\r\n<table id=\"eip-id1168468649947\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>The sum of [latex]\u22129[\/latex] and [latex]5[\/latex] indicates addition.<\/td>\r\n<td>the sum of [latex]-9[\/latex] and [latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate.<\/td>\r\n<td>[latex]-9+5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nNow you can try a similar problem.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145027&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\nIn the next example we add another term to the expression that is being translated. The result is an expression that contains three terms that are added or subtracted.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and simplify: the sum of [latex]8[\/latex] and [latex]-12[\/latex], increased by [latex]3[\/latex].\r\n[reveal-answer q=\"511380\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"511380\"]\r\n\r\nSolution:\r\nThe phrase <em>increased by<\/em> indicates addition.\r\n<table id=\"eip-id1168468229407\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>The sum of [latex]8[\/latex] and [latex]-12[\/latex] , increased by [latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate.<\/td>\r\n<td>[latex]\\left[8+\\left(-12\\right)\\right]+3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-4+3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]-1[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow you can try a similar problem.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145028&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\n<h2>Add Integers in Applications<\/h2>\r\nRecall that we were introduced to some situations in everyday life that use positive and negative numbers, such as temperatures, banking, and sports. For example, a debt of [latex]$5[\/latex] could be represented as [latex]-$5[\/latex]. Let\u2019s practice translating and solving a few applications.\r\n\r\nSolving applications is easy if we have a plan. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe temperature in Buffalo, NY, one morning started at [latex]7[\/latex] degrees below zero Fahrenheit. By noon, it had warmed up [latex]12[\/latex] degrees. What was the temperature at noon?\r\n[reveal-answer q=\"787450\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"787450\"]\r\n\r\nSolution:\r\nWe are asked to find the temperature at noon.\r\n<table id=\"eip-id1168469630355\" class=\"unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write a phrase for the temperature.<\/td>\r\n<td>The temperature warmed up 12 degrees from 7 degrees below zero.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to math notation.<\/td>\r\n<td>[latex]\u22127 + 12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence to answer the question.<\/td>\r\n<td>The temperature at noon was [latex]5[\/latex] degrees Fahrenheit.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow you can try a similar problem.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145032&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<iframe id=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145033&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\nIn the following video we show a similar example.\r\n\r\nhttps:\/\/youtu.be\/Ozqs2JdnOI8\r\n\r\nIn the next example, a football team gaining and losing yardage can be represented with positive and negative numbers.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nA football team took possession of the football on their [latex]42[\/latex]-yard line. In the next three plays, they lost [latex]\\text{6 yards,}[\/latex] gained [latex]4[\/latex] yards and then lost [latex]8[\/latex] yards. On what yard line was the ball at the end of those three plays?\r\n[reveal-answer q=\"924891\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"924891\"]\r\n\r\nSolution:\r\nWe are asked to find the yard line the ball was on at the end of three plays.\r\n<table id=\"eip-id1168468536362\" class=\"unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write a word phrase for the position of the ball.<\/td>\r\n<td>Start at [latex]42[\/latex], then lose [latex]6[\/latex], gain [latex]4[\/latex], lose [latex]8[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to math notation.<\/td>\r\n<td>[latex]42-6+4\u22128[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]32[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence to answer the question.<\/td>\r\n<td>At the end of the three plays, the ball is on the [latex]32[\/latex]-yard line.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow you can try a similar problem.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom5\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145035&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\nThe following video shows more examples of translating expressions that involve integers, and simplifying the result.\r\n\r\nhttps:\/\/youtu.be\/Cv3cIoiSUtk","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate word phrases to algebraic expressions<\/li>\n<li>Simplify algebraic expressions using the order of operations<\/li>\n<li>Add integers in application problems<\/li>\n<\/ul>\n<\/div>\n<h3>Translate Word Phrases to Algebraic Expressions<\/h3>\n<p>All our earlier work translating word phrases to algebra also applies to expressions that include both positive and negative numbers. Remember that the phrase <em>the sum<\/em> indicates addition.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and simplify: the sum of [latex]-9[\/latex] and [latex]5[\/latex].<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168468649947\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>The sum of [latex]\u22129[\/latex] and [latex]5[\/latex] indicates addition.<\/td>\n<td>the sum of [latex]-9[\/latex] and [latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]-9+5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Now you can try a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145027&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>In the next example we add another term to the expression that is being translated. The result is an expression that contains three terms that are added or subtracted.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and simplify: the sum of [latex]8[\/latex] and [latex]-12[\/latex], increased by [latex]3[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q511380\">Show Solution<\/span><\/p>\n<div id=\"q511380\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe phrase <em>increased by<\/em> indicates addition.<\/p>\n<table id=\"eip-id1168468229407\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>The sum of [latex]8[\/latex] and [latex]-12[\/latex] , increased by [latex]3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]\\left[8+\\left(-12\\right)\\right]+3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-4+3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]-1[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145028&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<h2>Add Integers in Applications<\/h2>\n<p>Recall that we were introduced to some situations in everyday life that use positive and negative numbers, such as temperatures, banking, and sports. For example, a debt of [latex]$5[\/latex] could be represented as [latex]-$5[\/latex]. Let\u2019s practice translating and solving a few applications.<\/p>\n<p>Solving applications is easy if we have a plan. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The temperature in Buffalo, NY, one morning started at [latex]7[\/latex] degrees below zero Fahrenheit. By noon, it had warmed up [latex]12[\/latex] degrees. What was the temperature at noon?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q787450\">Show Solution<\/span><\/p>\n<div id=\"q787450\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe are asked to find the temperature at noon.<\/p>\n<table id=\"eip-id1168469630355\" class=\"unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>Write a phrase for the temperature.<\/td>\n<td>The temperature warmed up 12 degrees from 7 degrees below zero.<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]\u22127 + 12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>The temperature at noon was [latex]5[\/latex] degrees Fahrenheit.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145032&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145033&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show a similar example.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Determine the Difference Between Two Temperatures (integers)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Ozqs2JdnOI8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In the next example, a football team gaining and losing yardage can be represented with positive and negative numbers.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>A football team took possession of the football on their [latex]42[\/latex]-yard line. In the next three plays, they lost [latex]\\text{6 yards,}[\/latex] gained [latex]4[\/latex] yards and then lost [latex]8[\/latex] yards. On what yard line was the ball at the end of those three plays?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q924891\">Show Solution<\/span><\/p>\n<div id=\"q924891\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe are asked to find the yard line the ball was on at the end of three plays.<\/p>\n<table id=\"eip-id1168468536362\" class=\"unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>Write a word phrase for the position of the ball.<\/td>\n<td>Start at [latex]42[\/latex], then lose [latex]6[\/latex], gain [latex]4[\/latex], lose [latex]8[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]42-6+4\u22128[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]32[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>At the end of the three plays, the ball is on the [latex]32[\/latex]-yard line.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom5\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145035&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>The following video shows more examples of translating expressions that involve integers, and simplifying the result.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Write and Determine a Sum Describing an Situation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Cv3cIoiSUtk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/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-9350\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Determine the Difference Between Two Temperatures (integers). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Ozqs2JdnOI8\">https:\/\/youtu.be\/Ozqs2JdnOI8<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Write and Determine a Sum Describing an Situation. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Cv3cIoiSUtk\">https:\/\/youtu.be\/Cv3cIoiSUtk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 145027, 145028, 145032, 145033, 145035. <strong>Authored by<\/strong>: Alyson Day. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":17535,"menu_order":11,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Ex: Determine the Difference Between Two Temperatures (integers)\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Ozqs2JdnOI8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Write and Determine a Sum Describing an Situation\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Cv3cIoiSUtk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 145027, 145028, 145032, 145033, 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