{"id":7106,"date":"2011-10-23T20:31:51","date_gmt":"2011-10-23T19:31:51","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7106"},"modified":"2022-01-15T19:18:57","modified_gmt":"2022-01-15T19:18:57","slug":"uma-caixa-com-tampa","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7106","title":{"rendered":"Uma caixa com tampa"},"content":{"rendered":"<p><ul id='GTTabs_ul_7106' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7106' class='GTTabs_curr'><a  id=\"7106_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7106' ><a  id=\"7106_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_7106'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1caixas.jpg\"><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=\"alignright wp-image-7107 size-full\" title=\"Caixa\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1caixas.jpg\" alt=\"\" width=\"127\" height=\"84\" \/><\/a>Uma caixa com tampa custa 1,20 \u20ac.<br \/>\nAo comprar 3 caixas e 5 tampas\u00a0gastamos 4,10 \u20ac.<br \/>\nQuanto custou cada tampa? E cada caixa?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7106' onClick='GTTabs_show(1,7106)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7106'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Uma caixa com tampa custa 1,20 \u20ac.<br \/>\nAo comprar 3 caixas e 5 tampas\u00a0gastamos 4,10 \u20ac.<br \/>\nQuanto custou cada tampa? E cada caixa?<\/p>\n<\/blockquote>\n<p>Seja:<\/p>\n<ul>\n<li>$c$: o pre\u00e7o de uma caixa, em euros;<\/li>\n<li>$t$: o pre\u00e7o de cada tampa, em euros.<\/li>\n<\/ul>\n<p>Equacionando o problema com um sistema de equa\u00e7\u00f5es e resolvendo-o, temos:<\/p>\n<p>\\[\\begin{array}{*{35}{l}} \u00a0\u00a0 \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 c+t=1,2\u00a0 \\\\ \u00a0\u00a0 3c+5t=4,1\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 c=1,2-t\u00a0 \\\\ \u00a0\u00a0 3,6-3t+5t=4,1\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 c=1,2-t\u00a0 \\\\ \u00a0\u00a0 2t=0,5\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 t=0,25\u00a0 \\\\ \u00a0\u00a0 c=0,95\u00a0 \\\\ \\end{array} \\right. &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \\end{array}\\]<\/p>\n<p>Portanto, cada caixa custa 0,95 \u20ac e cada tampa custa 0,25 \u20ac.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7106' onClick='GTTabs_show(0,7106)'>&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. Ao comprar 3 caixas e 5 tampas\u00a0gastamos 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":[213,97,240],"tags":[426,243],"series":[],"class_list":["post-7106","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-sistemas-de-equacoes","tag-9-o-ano","tag-sistemas-de-equacoes-2"],"views":2797,"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\/7106","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=7106"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7106\/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=7106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7106"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}