{"id":6776,"date":"2011-04-14T00:20:38","date_gmt":"2011-04-13T23:20:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6776"},"modified":"2022-01-18T02:25:13","modified_gmt":"2022-01-18T02:25:13","slug":"a-um-certo-numero","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6776","title":{"rendered":"A um certo n\u00famero"},"content":{"rendered":"<p><ul id='GTTabs_ul_6776' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6776' class='GTTabs_curr'><a  id=\"6776_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6776' ><a  id=\"6776_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_6776'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A um certo n\u00famero adicionou-se $\\frac{2}{3}$ do n\u00famero.<\/p>\n<p>A essa soma subtraiu-se $\\frac{1}{3}$ da soma, tendo-se obtido $10$.<\/p>\n<p>Qual \u00e9 o n\u00famero?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6776' onClick='GTTabs_show(1,6776)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6776'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>\u00a0Designando esse n\u00famero por x, temos:<\/p>\n<ul>\n<li>Dois ter\u00e7os do n\u00famero: $\\frac{2x}{3}$<\/li>\n<li>Essa soma: $x+\\frac{2x}{3}$<\/li>\n<li>Um ter\u00e7o da soma: $\\frac{1}{3}(x+\\frac{2x}{3})$<\/li>\n<\/ul>\n<p>Assim, temos:<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\n(x+\\frac{2x}{3})-\\frac{1}{3}(x+\\frac{2x}{3})=10 &amp; \\Leftrightarrow\u00a0 &amp; \\underset{(9)}{\\mathop{x}}\\,+\\frac{2x}{\\underset{(3)}{\\mathop{3}}\\,}-\\frac{x}{\\underset{(3)}{\\mathop{3}}\\,}-\\frac{2x}{\\underset{(1)}{\\mathop{9}}\\,}=\\underset{(9)}{\\mathop{10}}\\,\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 9x+6x-3x-2x=90\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 10x=90\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=9\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Portanto, o n\u00famero procurado \u00e9 9.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6776' onClick='GTTabs_show(0,6776)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A um certo n\u00famero adicionou-se $\\frac{2}{3}$ do n\u00famero. A essa soma subtraiu-se $\\frac{1}{3}$ da soma, tendo-se obtido $10$. Qual \u00e9 o n\u00famero? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20586,"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-6776","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-do-1--grau","tag-equacao"],"views":2137,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8V2Pag057-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6776","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=6776"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6776\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20586"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6776"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6776"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6776"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6776"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}