{"id":26119,"date":"2023-05-26T22:13:24","date_gmt":"2023-05-26T21:13:24","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26119"},"modified":"2023-05-27T00:24:34","modified_gmt":"2023-05-26T23:24:34","slug":"a-idade-do-diogo-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26119","title":{"rendered":"A idade do Diogo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26119' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26119' class='GTTabs_curr'><a  id=\"26119_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26119' ><a  id=\"26119_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_26119'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O Diogo tem \\(\\frac{1}{3}\\) da idade do pai. Daqui a 2 anos, a soma das idades dos dois \u00e9 60 anos.<\/p>\n<p>Quantos anos tem o Diogo?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26119' onClick='GTTabs_show(1,26119)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26119'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>O Diogo tem \\(\\frac{1}{3}\\) da idade do pai. Daqui a 2 anos, a soma das idades dos dois \u00e9 60 anos.<\/p>\n<p>Quantos anos tem o Diogo?<\/p>\n<\/blockquote>\n<p><br \/><br \/>Designemos a idade atual do Diogo por <em>d<\/em> e a idade atual do pai por <em>p<\/em>, ambas em anos.<\/p>\n<p>Equacionando o problema e resolvendo o sistema de equa\u00e7\u00f5es, temos: \\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{d = \\frac{1}{3}p}\\\\{\\left( {d + 2} \\right) + \\left( {p + 2} \\right) = 60}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{p = 3d}\\\\{d + 2 + 3d + 2 = 60}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{4d = 56}\\\\{p = 3d}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{d = 14}\\\\{p = 42}\\end{array}} \\right.}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>Portanto, o Diogo tem 14 anos e o pai tem 42 anos.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26119' onClick='GTTabs_show(0,26119)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Diogo tem \\(\\frac{1}{3}\\) da idade do pai. Daqui a 2 anos, a soma das idades dos dois \u00e9 60 anos. Quantos anos tem o Diogo? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14114,"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-26119","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":72,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat56.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26119","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=26119"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26119\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26119"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}