{"id":10358,"date":"2012-10-13T18:57:03","date_gmt":"2012-10-13T17:57:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10358"},"modified":"2022-01-20T00:12:52","modified_gmt":"2022-01-20T00:12:52","slug":"o-dinheiro-do-pedro","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10358","title":{"rendered":"O dinheiro do Pedro"},"content":{"rendered":"<p><ul id='GTTabs_ul_10358' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10358' class='GTTabs_curr'><a  id=\"10358_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10358' ><a  id=\"10358_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_10358'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/moedas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10375\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10375\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/moedas.jpg\" data-orig-size=\"540,574\" 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=\"Moedas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/moedas.jpg\" class=\"alignright wp-image-10375\" title=\"Moedas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/moedas.jpg\" alt=\"\" width=\"240\" height=\"255\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/moedas.jpg 540w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/moedas-282x300.jpg 282w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/moedas-141x150.jpg 141w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/moedas-400x425.jpg 400w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/p>\n<p>O Pedro tem o triplo do dinheiro da sua irm\u00e3 Ana.<\/p>\n<p>Ao todo, os dois irm\u00e3os t\u00eam $234$ \u20ac.<\/p>\n<p>Que quantia tem o Pedro? Explica como chegaste \u00e0 tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10358' onClick='GTTabs_show(1,10358)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10358'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Comecemos por criar uma tabela, atribuindo \u00e0 Ana uma determinada quantia de dinheiro e preenchendo as c\u00e9lulas\u00a0restantes dessa linha:<\/p>\n<table class=\" aligncenter\" style=\"width: 300px;\" border=\"0\" cellspacing=\"10\" cellpadding=\"0\" align=\"center\">\n<caption>Quantias envolvidas<br \/>\n(em euros)<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">ANA<\/td>\n<td style=\"text-align: center;\">PEDRO<\/td>\n<td style=\"text-align: center;\">TOTAL<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$1$<\/td>\n<td style=\"text-align: center;\">$3$<\/td>\n<td style=\"text-align: center;\">$4$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$5$<\/td>\n<td style=\"text-align: center;\">$15$<\/td>\n<td style=\"text-align: center;\">$20$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$100$<\/td>\n<td style=\"text-align: center;\">$300$<\/td>\n<td style=\"text-align: center;\">$400$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$530$<\/td>\n<td style=\"text-align: center;\">$1590$<\/td>\n<td style=\"text-align: center;\">$2120$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$600$<\/td>\n<td style=\"text-align: center;\">$1800$<\/td>\n<td style=\"text-align: center;\">$2400$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">&#8230;<\/td>\n<td style=\"text-align: center;\">&#8230;<\/td>\n<td style=\"text-align: center;\">&#8230;<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$(?)$<\/td>\n<td style=\"text-align: center;\">$(??)$<\/td>\n<td style=\"text-align: center;\"><span style=\"color: #008000;\"><strong>$2348$<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">&#8230;<\/td>\n<td style=\"text-align: center;\">&#8230;<\/td>\n<td style=\"text-align: center;\">&#8230;<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><strong>Triplo<\/strong><br \/>\nda quantia da Ana<\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\"><strong>Qu\u00e1druplo<\/strong><\/span><br \/>\nda quantia da Ana<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Numa\u00a0primeira tentativa podemos ir preenchendo a tabela, de forma\u00a0a totalidade das quantias envolvidas dar $2348$ euros.<\/p>\n<p>No entanto, numa an\u00e1lise mais cuidada da tabela, podemos concluir que o TOTAL das quantias envolvidas \u00e9 o QU\u00c1DRUPLO da quantia da Ana.<\/p>\n<p>Isto \u00e9, verifica-se a rela\u00e7\u00e3o: $4 \\times \\left( ? \\right) = 2348$.<\/p>\n<p>Desta igualdade, podemos obter:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left( ? \\right)}&amp; = &amp;{2348 \\div 4} \\\\ \u00a0 {}&amp; = &amp;{587} \\end{array}$$<\/p>\n<p>Isto \u00e9, a Ana tem a quantia de $587$ euros.<\/p>\n<p>Como o Pedro possui o triplo da quantia da Ana, vem:<br \/>\n$$\\begin{array}{*{20}{l}} \u00a0 {\\left( {??} \\right)}&amp; = &amp;{3 \\times 587} \\\\ \u00a0 {}&amp; = &amp;{1761} \\end{array}$$<\/p>\n<p>Portanto, o Pedro possui a quantia de $1761$ euros.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10358' onClick='GTTabs_show(0,10358)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Pedro tem o triplo do dinheiro da sua irm\u00e3 Ana. Ao todo, os dois irm\u00e3os t\u00eam $234$ \u20ac. Que quantia tem o Pedro? Explica como chegaste \u00e0 tua resposta. Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20708,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[317,97,318],"tags":[428,320,327],"series":[],"class_list":["post-10358","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-7-o-ano","category-aplicando","category-numeros-inteiros","tag-7-o-ano","tag-multiplicacao","tag-propriedades-da-multiplicacao"],"views":1176,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/7V1Pag019-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10358","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=10358"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10358\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20708"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10358"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10358"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10358"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10358"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}