{"id":25915,"date":"2023-05-21T19:36:46","date_gmt":"2023-05-21T18:36:46","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25915"},"modified":"2023-05-21T20:12:00","modified_gmt":"2023-05-21T19:12:00","slug":"a-ana-comprou-sanduiches-para-alguns-colegas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25915","title":{"rendered":"A Ana comprou sandu\u00edches para alguns colegas"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25915' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25915' class='GTTabs_curr'><a  id=\"25915_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25915' ><a  id=\"25915_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_25915'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera o seguinte problema:<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25917\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25917\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3.png\" data-orig-size=\"539,451\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag202-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3.png\" class=\"aligncenter wp-image-25917\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3-300x251.png\" alt=\"\" width=\"340\" height=\"284\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3-300x251.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3.png 539w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a><\/p>\n<ol>\n<li>Escreve uma equa\u00e7\u00e3o do 1.\u00ba grau que permita completar o sistema que se segue, de modo que este traduza o problema.<br \/>\\[\\left\\{ {\\begin{array}{*{20}{l}}{x = y + 3}\\\\ \\cdots \\end{array}} \\right.\\]<\/li>\n<li>Que resposta darias a este problema?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25915' onClick='GTTabs_show(1,25915)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25915'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Considera o seguinte problema:<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25917\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25917\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3.png\" data-orig-size=\"539,451\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag202-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3.png\" class=\"wp-image-25917 alignright\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3-300x251.png\" alt=\"\" width=\"340\" height=\"284\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3-300x251.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3.png 539w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a><\/p>\n<ol>\n<li>\n<blockquote>Escreve uma equa\u00e7\u00e3o do 1.\u00ba grau que permita completar o sistema que se segue, de modo que este traduza o problema.\\[\\left\\{ {\\begin{array}{*{20}{l}}{x = y + 3}\\\\ \\cdots \\end{array}} \\right.\\]<\/blockquote>\n<\/li>\n<li>\n<blockquote>Que resposta darias a este problema?<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>Como a Ana &#8220;comprou mais tr\u00eas sandu\u00edches do que sumos&#8221;, identifica-se que, da 1.\u00aa equa\u00e7\u00e3o do sistema, <em>x<\/em> traduz o n\u00famero de sandu\u00edches e <em>y<\/em> traduz o n\u00famero de sumos que ela comprou.<br \/>Assim, o custo, em euros, das sandu\u00edches \u00e9 dado por \\(0,8x\\) e o custo dos sumos \u00e9 dado por \\(0,3y\\).<br \/>Logo, uma equa\u00e7\u00e3o que permite completar o sistema \u00e9 \\(0,8x + 0,3y = 4,6\\).<br \/><br \/><\/li>\n<li>Resolvendo o sistema, vem:<br \/>\\[\\begin{array}{*{20}{c}}{\\left\\{ {\\begin{array}{*{20}{l}}{x = y + 3}\\\\{0,8x + 0,3y = 4,6}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = y + 3}\\\\{0,8\\left( {y + 3} \\right) + 0,3y = 4,6}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = y + 3}\\\\{1,1y = 2,2}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = 2}\\\\{x = 5}\\end{array}} \\right.}\\end{array}\\]Portanto, a Ana comprou 5 sandu\u00edches e 2 sumos.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25915' onClick='GTTabs_show(0,25915)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera o seguinte problema: Escreve uma equa\u00e7\u00e3o do 1.\u00ba grau que permita completar o sistema que se segue, de modo que este traduza o problema.\\[\\left\\{ {\\begin{array}{*{20}{l}}{x = y + 3}\\\\ \\cdots&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25918,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,345,239],"series":[],"class_list":["post-25915","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-literais-e-sistemas","tag-8-o-ano","tag-funcao-afim","tag-sistema-de-equacoes"],"views":58,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag202-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25915","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=25915"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25915\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25918"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25915"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25915"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}