{"id":7108,"date":"2011-10-23T21:10:13","date_gmt":"2011-10-23T20:10:13","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7108"},"modified":"2022-01-15T18:47:59","modified_gmt":"2022-01-15T18:47:59","slug":"a-idade-do-diogo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7108","title":{"rendered":"A idade do Diogo"},"content":{"rendered":"<p><ul id='GTTabs_ul_7108' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7108' class='GTTabs_curr'><a  id=\"7108_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7108' ><a  id=\"7108_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_7108'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/rapaz.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7109\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7109\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/rapaz.jpg\" data-orig-size=\"193,261\" 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=\"Diogo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/rapaz.jpg\" class=\"alignright wp-image-7109\" title=\"Diogo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/rapaz.jpg\" alt=\"\" width=\"170\" height=\"230\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/rapaz.jpg 193w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/rapaz-110x150.jpg 110w\" sizes=\"auto, (max-width: 170px) 100vw, 170px\" \/><\/a>O Diogo tem um ter\u00e7o da idade do pai.<br \/>\nDaqui a dois anos, a soma das idades dos dois perfaz sessenta anos.<br \/>\nQuantos anos tem o Diogo?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7108' onClick='GTTabs_show(1,7108)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7108'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>O Diogo tem um ter\u00e7o da idade do pai.<br \/>\nDaqui a dois anos, a soma das idades dos dois perfaz sessenta anos.<br \/>\nQuantos anos tem o Diogo?<\/p>\n<\/blockquote>\n<p>Seja:<\/p>\n<ul>\n<li>$d$: a idade actual do Diogo, em anos;<\/li>\n<li>$p$: a idade actual do pai do Diogo, em anos.<\/li>\n<\/ul>\n<p>Equacionando o problema atrav\u00e9s de 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 d=\\frac{1}{3}p\u00a0 \\\\ \u00a0\u00a0 (d+2)+(p+2)=60\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 d=\\frac{1}{3}p\u00a0 \\\\ \u00a0\u00a0 d+p=56\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 d=\\frac{1}{3}p\u00a0 \\\\ \u00a0\u00a0 \\frac{1}{3}p+p=56\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 d=\\frac{1}{3}p\u00a0 \\\\ \u00a0\u00a0 p+3p=168\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 p=42\u00a0 \\\\ \u00a0\u00a0 d=14\u00a0 \\\\ \\end{array} \\right. &amp; {}\u00a0 \\\\ \\end{array}\\]<\/p>\n<p>O Diogo tem 14 anos (e o pai tem 42 anos).<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7108' onClick='GTTabs_show(0,7108)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Diogo tem um ter\u00e7o da idade do pai. Daqui a dois anos, a soma das idades dos dois perfaz sessenta anos. Quantos anos tem o Diogo? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20278,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,240],"tags":[426,239],"series":[],"class_list":["post-7108","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-sistema-de-equacoes"],"views":2191,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/9V1Pag050-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7108","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=7108"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7108\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20278"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7108"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7108"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7108"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7108"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}