{"id":7110,"date":"2011-10-23T21:22:55","date_gmt":"2011-10-23T20:22:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7110"},"modified":"2022-01-15T18:38:23","modified_gmt":"2022-01-15T18:38:23","slug":"violao-e-violino","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7110","title":{"rendered":"Viol\u00e3o e violino"},"content":{"rendered":"<p><ul id='GTTabs_ul_7110' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7110' class='GTTabs_curr'><a  id=\"7110_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7110' ><a  id=\"7110_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_7110'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/violino.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7111\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7111\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/violino.jpg\" data-orig-size=\"350,300\" 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=\"Violino\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/violino.jpg\" class=\"alignright size-full wp-image-7111\" title=\"Violino\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/violino.jpg\" alt=\"\" width=\"210\" height=\"180\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/violino.jpg 350w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/violino-300x257.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/violino-150x128.jpg 150w\" sizes=\"auto, (max-width: 210px) 100vw, 210px\" \/><\/a>Os alunos de um conservat\u00f3rio de m\u00fasica v\u00e3o fazer uma apresenta\u00e7\u00e3o no pr\u00f3ximo s\u00e1bado.<br \/>\nO grupo \u00e9 formado por vinte pessoas, que tocam violino e viol\u00e3o.<br \/>\nSabe-se que um viol\u00e3o tem seis cordas, um violino tem quatro cordas e o n\u00famero total de cordas desse grupo \u00e9 cento e quatro.<\/p>\n<p>Quantos viol\u00f5es e violinos estar\u00e3o em palco?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7110' onClick='GTTabs_show(1,7110)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7110'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Os alunos de um conservat\u00f3rio de m\u00fasica v\u00e3o fazer uma apresenta\u00e7\u00e3o no pr\u00f3ximo s\u00e1bado.<br \/>\nO grupo \u00e9 formado por vinte pessoas, que tocam violino e viol\u00e3o.<br \/>\nSabe-se que um viol\u00e3o tem seis cordas, um violino tem quatro cordas e o n\u00famero total de cordas desse grupo \u00e9 cento e quatro.<br \/>\nQuantos viol\u00f5es e violinos estar\u00e3o em palco?<\/p>\n<\/blockquote>\n<p>Seja:<\/p>\n<ul>\n<li>$x$: n\u00famero de violinos do grupo;<\/li>\n<li>$y$: n\u00famero de viol\u00f5es do grupo.<\/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 x+y=20\u00a0 \\\\ \u00a0\u00a0 4x+6y=104\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 y=20-x\u00a0 \\\\ \u00a0\u00a0 4x+120-6x=104\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 y=20-x\u00a0 \\\\ \u00a0\u00a0 2x=16\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 x=8\u00a0 \\\\ \u00a0\u00a0 y=12\u00a0 \\\\ \\end{array} \\right. &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \\end{array}\\]<\/p>\n<p>Estar\u00e3o em palco 8 violinos e 12 viol\u00f5es.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7110' onClick='GTTabs_show(0,7110)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Os alunos de um conservat\u00f3rio de m\u00fasica v\u00e3o fazer uma apresenta\u00e7\u00e3o no pr\u00f3ximo s\u00e1bado. O grupo \u00e9 formado por vinte pessoas, que tocam violino e viol\u00e3o. Sabe-se que um viol\u00e3o tem&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20276,"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-7110","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":3493,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/9V1Pag050-9_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7110","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=7110"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7110\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20276"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7110"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}