{"id":26114,"date":"2023-05-26T18:08:42","date_gmt":"2023-05-26T17:08:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26114"},"modified":"2023-05-26T21:24:08","modified_gmt":"2023-05-26T20:24:08","slug":"uma-caixa-com-tampa-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26114","title":{"rendered":"Uma caixa com tampa"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26114' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26114' class='GTTabs_curr'><a  id=\"26114_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26114' ><a  id=\"26114_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_26114'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7107\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7107\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1caixas.jpg\" data-orig-size=\"127,84\" 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;}\" data-image-title=\"Caixa\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1caixas.jpg\" class=\"size-full wp-image-7107 alignright\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1caixas.jpg\" alt=\"\" width=\"127\" height=\"84\" \/>Uma caixa com tampa custa 1,20 \u20ac.<br \/>\u00a0Ao comprar 3 caixas e 5 tampas gast\u00e1mos 4,10 \u20ac.<\/p>\n<p>Quanto custou cada tampa? E cada caixa?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26114' onClick='GTTabs_show(1,26114)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26114'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7107\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7107\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1caixas.jpg\" data-orig-size=\"127,84\" 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;}\" data-image-title=\"Caixa\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1caixas.jpg\" class=\"size-full wp-image-7107 alignright\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1caixas.jpg\" alt=\"\" width=\"127\" height=\"84\" \/>Uma caixa com tampa custa 1,20 \u20ac.<br \/>\u00a0Ao comprar 3 caixas e 5 tampas gast\u00e1mos 4,10 \u20ac.<\/p>\n<p>Quanto custou cada tampa? E cada caixa?<\/p>\n<\/blockquote>\n<p><br \/>Designemos por <em>c<\/em> o pre\u00e7o de cada caixa e por <em>t<\/em> o pre\u00e7o de cada tampa, em euros.<\/p>\n<p>Equacionando o problema e resolvendo o sistema de equa\u00e7\u00f5es, temos: \\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{c + t = 1,2}\\\\{3c + 5t = 4,1}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{c = 1,2 &#8211; t}\\\\{3\\left( {1,2 &#8211; t} \\right) + 5t = 4,1}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{c = 1,2 &#8211; t}\\\\{3,6 &#8211; 3t + 5t = 4,1}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{2t = 0,5}\\\\{c = 1,2 &#8211; t}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{t = 0,25}\\\\{c = 0,95}\\end{array}} \\right.}&amp;{}\\end{array}\\]<\/p>\n<p>Portanto, cada tampa custou \\({0,25}\\) \u20ac e cada caixa custou \\({0,95}\\) \u20ac.<\/p>\n\n\n\n<p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26114' onClick='GTTabs_show(0,26114)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Uma caixa com tampa custa 1,20 \u20ac.\u00a0Ao comprar 3 caixas e 5 tampas gast\u00e1mos 4,10 \u20ac. Quanto custou cada tampa? E cada caixa? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20280,"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-26114","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":68,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/9V1Pag050-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26114","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=26114"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26114\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20280"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26114"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}