{"id":26122,"date":"2023-05-27T00:39:37","date_gmt":"2023-05-26T23:39:37","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26122"},"modified":"2023-05-27T01:16:33","modified_gmt":"2023-05-27T00:16:33","slug":"quantos-violoes-e-quantos-violinos-estarao-em-palco","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26122","title":{"rendered":"Quantos viol\u00f5es e quantos violinos estar\u00e3o em palco?"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26122' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26122' class='GTTabs_curr'><a  id=\"26122_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26122' ><a  id=\"26122_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_26122'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>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 20 pessoas que tocam viol\u00e3o e violino. Sabendo-se que um viol\u00e3o tem 6 cordas, um violino tem 4 cordas e o n\u00famero total de cordas desse grupo \u00e9 104, quantos viol\u00f5es e quantos violinos estar\u00e3o em palco?<\/p>\n<div id=\"attachment_26126\" style=\"width: 870px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-26126\" data-attachment-id=\"26126\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26126\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/A-Camerata-de-Cordas-da-UFC-scaled.jpg\" data-orig-size=\"2560,1637\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;5&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;NIKON D3400&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1535994635&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;24&quot;,&quot;iso&quot;:&quot;900&quot;,&quot;shutter_speed&quot;:&quot;0.01&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"A-Camerata-de-Cordas-da-UFC\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/A-Camerata-de-Cordas-da-UFC-1024x655.jpg\" class=\"wp-image-26126\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/A-Camerata-de-Cordas-da-UFC-300x192.jpg\" alt=\"\" width=\"860\" height=\"550\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/A-Camerata-de-Cordas-da-UFC-300x192.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/A-Camerata-de-Cordas-da-UFC-1024x655.jpg 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/A-Camerata-de-Cordas-da-UFC-768x491.jpg 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/A-Camerata-de-Cordas-da-UFC-1536x982.jpg 1536w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/A-Camerata-de-Cordas-da-UFC-2048x1309.jpg 2048w\" sizes=\"auto, (max-width: 860px) 100vw, 860px\" \/><p id=\"caption-attachment-26126\" class=\"wp-caption-text\">Camerata de Cordas da Universidade Federal do Cear\u00e1 (UFC) <br \/><a href=\"https:\/\/www.facebook.com\/camerataufc\/?locale=pt_BR\" target=\"_blank\" rel=\"noopener\">https:\/\/www.facebook.com\/camerataufc\/?locale=pt_BR<\/a><\/p><\/div>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26122' onClick='GTTabs_show(1,26122)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26122'>\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. O grupo \u00e9 formado por 20 pessoas que tocam viol\u00e3o e violino. Sabendo-se que um viol\u00e3o tem 6 cordas, um violino tem 4 cordas e o n\u00famero total de cordas desse grupo \u00e9 104, quantos viol\u00f5es e quantos violinos estar\u00e3o em palco?<\/p>\n<\/blockquote>\n<p><br \/>Designemos por <em>x<\/em> o n\u00famero de viol\u00f5es e por <em>y<\/em> o n\u00famero de violinos.<\/p>\n<p>Equacionando o problema e resolvendo o sistema de equa\u00e7\u00f5es, temos: \\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 20}\\\\{6x + 4y = 104}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = 20 &#8211; y}\\\\{120 &#8211; 6y + 4y = 104}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{2y = 16}\\\\{x = 20 &#8211; y}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = 8}\\\\{x = 12}\\end{array}} \\right.}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>Portanto, estar\u00e3o em palco 12 viol\u00f5es e 8 violinos.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26122' onClick='GTTabs_show(0,26122)'>&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 20 pessoas que tocam viol\u00e3o e violino. Sabendo-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":[100,97,714],"tags":[424,345,239],"series":[],"class_list":["post-26122","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":71,"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\/26122","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=26122"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26122\/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=26122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26122"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}