{"id":3252,"date":"2010-09-30T22:46:14","date_gmt":"2010-09-30T21:46:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3252"},"modified":"2022-01-18T21:26:14","modified_gmt":"2022-01-18T21:26:14","slug":"canetas-e-lapis","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3252","title":{"rendered":"Canetas e l\u00e1pis"},"content":{"rendered":"<p><ul id='GTTabs_ul_3252' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3252' class='GTTabs_curr'><a  id=\"3252_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3252' ><a  id=\"3252_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_3252'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/ColouredPencilsCircle.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3516\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3516\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/ColouredPencilsCircle.jpg\" data-orig-size=\"700,467\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;10&quot;,&quot;credit&quot;:&quot;Marc Pinter &lt;marc@marcpinter.com&gt;&quot;,&quot;camera&quot;:&quot;Canon EOS 5D&quot;,&quot;caption&quot;:&quot;Colored Pencils arranged to form a white copyspace circle&quot;,&quot;created_timestamp&quot;:&quot;1217707176&quot;,&quot;copyright&quot;:&quot;(c) 2008 Marc Pinter Photography\\n\\nhttp:\/\/www.marcpinter.com&quot;,&quot;focal_length&quot;:&quot;100&quot;,&quot;iso&quot;:&quot;100&quot;,&quot;shutter_speed&quot;:&quot;0.005&quot;,&quot;title&quot;:&quot;Colored Pencils&quot;}\" data-image-title=\"L\u00e1pis\" data-image-description=\"&lt;p&gt;Colored Pencils arranged to form a white copyspace circle&lt;\/p&gt;\n\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/ColouredPencilsCircle.jpg\" class=\"alignright size-thumbnail wp-image-3516\" title=\"L\u00e1pis\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/ColouredPencilsCircle-150x150.jpg\" alt=\"\" width=\"150\" height=\"150\" \/><\/a>Uma caneta custa mais 1 \u20ac do que um l\u00e1pis. Comprei duas canetas e quatro l\u00e1pis e gastei 3,2 \u20ac.<\/p>\n<ol>\n<li>Escreve uma equa\u00e7\u00e3o que traduza o problema.<\/li>\n<li>Quanto custa cada l\u00e1pis?<\/li>\n<li>Qual \u00e9 o custo de cada caneta?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3252' onClick='GTTabs_show(1,3252)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3252'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Consideremos:<br \/>\n&#8211; <span style=\"text-decoration: underline;\">Custo de um l\u00e1pis<\/span> (em euros): $x$<\/p>\n<p>Logo:<br \/>\n&#8211; <span style=\"text-decoration: underline;\">Custo de uma caneta<\/span> (em euros): $x+1$<\/p>\n<p>Assim, o problema pode ser traduzido pela equa\u00e7\u00e3o seguinte:\u00a0\\[\\underset{custo\\text{ }das\\text{ }duas\\text{ }canetas}{\\mathop 2(x+1)}\\,+\\underset{custo\\text{ }dos\\text{ }quatro\\text{ }l\\acute{a}pis}{\\mathop 4x}\\,=\\underset{valor\\text{ }da\\text{ }compra}{\\mathop 3,2}\\,\\]<br \/>\n\u00ad<\/p>\n<\/li>\n<li>Resolvendo a equa\u00e7\u00e3o, temos: \\[\\begin{array}{*{35}{l}} \u00a0\u00a0 2(x+1)+4x=3,2 &amp; \\Leftrightarrow\u00a0 &amp; 2x+2+4x=3,2\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; 6x=3,2-2\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{6x}{6}=\\frac{1,2}{6}\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; x=0,2\u00a0 \\\\ \\end{array}\\]<br \/>\nPortanto, cada l\u00e1pis custa 0,20 \u20ac.<br \/>\n\u00ad<\/li>\n<li>Cada caneta custa 1,20 \u20ac (0,20 \u20ac + 1,00 \u20ac).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3252' onClick='GTTabs_show(0,3252)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Uma caneta custa mais 1 \u20ac do que um l\u00e1pis. Comprei duas canetas e quatro l\u00e1pis e gastei 3,2 \u20ac. Escreve uma equa\u00e7\u00e3o que traduza o problema. Quanto custa cada l\u00e1pis?&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20605,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,101],"tags":[424,425],"series":[],"class_list":["post-3252","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes","tag-8-o-ano","tag-equacoes"],"views":1856,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/7V2Pag066-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3252","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=3252"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3252\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20605"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3252"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}