{"id":14754,"date":"2018-04-22T11:22:35","date_gmt":"2018-04-22T10:22:35","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14754"},"modified":"2022-01-09T23:21:02","modified_gmt":"2022-01-09T23:21:02","slug":"a-viagem-aos-jogos-olimpicos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14754","title":{"rendered":"A viagem aos Jogos Ol\u00edmpicos"},"content":{"rendered":"<p><ul id='GTTabs_ul_14754' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14754' class='GTTabs_curr'><a  id=\"14754_0\" onMouseOver=\"GTTabsShowLinks('Enumciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enumciado<\/a><\/li>\n<li id='GTTabs_li_1_14754' ><a  id=\"14754_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_14754'>\n<span class='GTTabs_titles'><b>Enumciado<\/b><\/span><\/p>\n<p>A viagem aos Jogos Ol\u00edmpicos vai custar ao clube desportivo 100 euros, mas o clube quer vender as rifas para a viagem de forma a ter 80 euros de lucro. As rifas ser\u00e3o todas vendidas e ao mesmo pre\u00e7o.<\/p>\n<p>A tabela seguinte representa a rela\u00e7\u00e3o entre o n\u00famero de rifas (<em>n<\/em>) que devem vender e o pre\u00e7o (<em>p<\/em>), em euros, de cada rifa.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14755\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14755\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9.png\" data-orig-size=\"589,151\" 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=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9.png\" class=\"aligncenter wp-image-14755\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9-300x77.png\" alt=\"\" width=\"320\" height=\"82\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9-300x77.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9.png 589w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a><\/p>\n<ol>\n<li>Qual \u00e9 o n\u00famero de rifas que deveriam ser vendidas para que o pre\u00e7o de cada uma fosse 1,5 euros?<\/li>\n<li>O n\u00famero de rifas (<em>n<\/em>) \u00e9 inversamente proporcional ao pre\u00e7o (<em>p<\/em>), em euros, de cada rifa.<br \/>\nQual \u00e9 a constante de proporcionalidade inversa? O que representa?<\/li>\n<li>Qual das express\u00f5es seguintes pode traduzir a rela\u00e7\u00e3o entre as vari\u00e1veis n\u00famero de rifas (<em>n<\/em>) e o pre\u00e7o (<em>p<\/em>), em euros, de cada rifa?<br \/>\n[<strong>A<\/strong>] \\(p = n \\times 180\\)\u00a0 \u00a0 \u00a0 [<strong>B<\/strong>] \\(p = n + 180\\)\u00a0 \u00a0 \u00a0 [<strong>C<\/strong>] \\(p = \\frac{n}{{180}}\\)\u00a0 \u00a0 \u00a0 [<strong>D<\/strong>]\u00a0\\(p = \\frac{{180}}{n}\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14754' onClick='GTTabs_show(1,14754)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14754'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14755\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14755\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9.png\" data-orig-size=\"589,151\" 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=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9.png\" class=\"aligncenter wp-image-14755\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9-300x77.png\" alt=\"\" width=\"320\" height=\"82\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9-300x77.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9.png 589w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a><\/p>\n<ol>\n<li>A receita da venda das rifas ter\u00e1 de ser 180 euros, de forma a ter 80 euros de lucro.<br \/>\nSe cada uma das rifas fosse vendida a 1,5 euros, deveriam ser vendidas \\(\\frac{{180}}{{1,5}} = 120\\) rifas.<br \/>\n\u00ad<\/li>\n<li>Como \\(n \\times p = 3 \\times 60 = 4 \\times 45 = 5 \\times 36 = &#8230; = 180\\), a constante de proporcionalidade inversa \u00e9 180.<br \/>\nA constante de proporcionalidade representa, em euros, a receita total da venda das rifas, de forma a garantir o referido lucro de 80 euros.<br \/>\n\u00ad<\/li>\n<li>J\u00e1 vimos, em 2., que\u00a0\\(n \\times p = 180\\), donde\u00a0\\(p = \\frac{{180}}{n}\\).<br \/>\nLogo, a alternativa correta \u00e9 a [D].<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14754' onClick='GTTabs_show(0,14754)'>&lt;&lt; Enumciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enumciado Resolu\u00e7\u00e3o Enumciado A viagem aos Jogos Ol\u00edmpicos vai custar ao clube desportivo 100 euros, mas o clube quer vender as rifas para a viagem de forma a ter 80 euros de lucro. As&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14757,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,250],"series":[],"class_list":["post-14754","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-9-o-ano","tag-proporcionalidade-inversa-2"],"views":3702,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-9a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14754","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=14754"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14754\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14757"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14754"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14754"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14754"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14754"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}