{"id":6786,"date":"2011-04-14T18:52:29","date_gmt":"2011-04-14T17:52:29","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6786"},"modified":"2022-01-18T02:41:47","modified_gmt":"2022-01-18T02:41:47","slug":"as-economias-do-nuno","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6786","title":{"rendered":"As economias do Nuno"},"content":{"rendered":"<p><ul id='GTTabs_ul_6786' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6786' class='GTTabs_curr'><a  id=\"6786_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6786' ><a  id=\"6786_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_6786'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/boy.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12277\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12277\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/boy.png\" data-orig-size=\"613,640\" 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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Boy\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/boy.png\" class=\"alignright wp-image-12277 size-medium\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/boy-287x300.png\" alt=\"Boy\" width=\"287\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/boy-287x300.png 287w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/boy.png 613w\" sizes=\"auto, (max-width: 287px) 100vw, 287px\" \/><\/a>O Nuno gasta $\\frac{2}{5}$\u00a0das suas economias e depois a quarta parte do que lhe resta. No fim, sobram-lhe ainda 10,80 euros.<\/p>\n<p>Quanto dinheiro tinha no in\u00edcio?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6786' onClick='GTTabs_show(1,6786)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6786'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>O Nuno gasta $\\frac{2}{5}$\u00a0das suas economias e depois a quarta parte do que lhe resta. No fim, sobram-lhe ainda 10,80 euros.<\/p>\n<\/blockquote>\n<p>Seja $x$ o dinheiro (em euros) inicial do Nuno.<\/p>\n<p>Assim, temos:<\/p>\n<ul>\n<li>Primeiro gasto: $\\frac{2x}{5}$<\/li>\n<li>O que resta ao fim do primeiro gasto: $x-\\frac{2x}{5}$<\/li>\n<li>Segundo gasto: $\\frac{1}{4}\\left( x-\\frac{2x}{5} \\right)$<\/li>\n<\/ul>\n<p>Logo, \\[\\begin{array}{*{35}{l}}<br \/>\n\\frac{2x}{5}+\\frac{1}{4}\\left( x-\\frac{2x}{5} \\right)+10,8=x &amp; \\Leftrightarrow\u00a0 &amp; \\frac{2x}{\\underset{(4)}{\\mathop{5}}\\,}+\\frac{x}{\\underset{(5)}{\\mathop{4}}\\,}-\\frac{x}{\\underset{(2)}{\\mathop{10}}\\,}+\\underset{(20)}{\\mathop{10,8}}\\,=\\underset{(20)}{\\mathop{x}}\\,\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 8x+5x-2x+216=20x\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 9x=216\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=24\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>No in\u00edcio, o Nuno tinha 24 euros.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6786' onClick='GTTabs_show(0,6786)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Nuno gasta $\\frac{2}{5}$\u00a0das suas economias e depois a quarta parte do que lhe resta. No fim, sobram-lhe ainda 10,80 euros. Quanto dinheiro tinha no in\u00edcio? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20591,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,159],"tags":[160],"series":[],"class_list":["post-6786","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-do-1--grau","tag-equacao"],"views":2063,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8V2Pag061-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6786","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=6786"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6786\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20591"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6786"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}