{"id":6778,"date":"2011-04-14T00:42:37","date_gmt":"2011-04-13T23:42:37","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6778"},"modified":"2022-01-18T02:29:33","modified_gmt":"2022-01-18T02:29:33","slug":"num-cabaz","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6778","title":{"rendered":"Num cabaz"},"content":{"rendered":"<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/cesta-de-fruta.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12279\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12279\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/cesta-de-fruta.png\" data-orig-size=\"895,648\" 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=\"Cesta de fruta\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/cesta-de-fruta.png\" class=\"alignright size-medium wp-image-12279\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/cesta-de-fruta-300x217.png\" alt=\"Cesta de fruta\" width=\"300\" height=\"217\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/cesta-de-fruta-300x217.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/cesta-de-fruta.png 895w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><ul id='GTTabs_ul_6778' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6778' class='GTTabs_curr'><a  id=\"6778_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6778' ><a  id=\"6778_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_6778'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Num cabaz h\u00e1 ma\u00e7\u00e3s, p\u00eassegos e bananas.<\/p>\n<p>O n\u00famero de ma\u00e7\u00e3s \u00e9 duplo do dos p\u00eassegos e o n\u00famero de bananas \u00e9 um ter\u00e7o do dos p\u00eassegos.<\/p>\n<p>Quantas s\u00e3o as pe\u00e7as de cada qualidade de fruta se o cabaz tiver 15 frutos?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6778' onClick='GTTabs_show(1,6778)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6778'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Designando o n\u00famero de p\u00eassegos por x, temos:<\/p>\n<ul>\n<li>N\u00famero de ma\u00e7\u00e3s: $2x$<\/li>\n<li>N\u00famero de bananas: $\\frac{x}{3}$<\/li>\n<\/ul>\n<p>Assim, vem:<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\nx+2x+\\frac{x}{3}=15 &amp; \\Leftrightarrow\u00a0 &amp; 3x+6x+x=45\\,\\,(\\text{Porqu }\\!\\!\\hat{\\mathrm{e}}\\!\\!\\text{ ?})\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 10x=45\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=4,5\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Como o n\u00famero de p\u00eassegos tem de ser um n\u00famero inteiro positivo, conclui-se que o problema \u00e9 imposs\u00edvel.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6778' onClick='GTTabs_show(0,6778)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Num cabaz h\u00e1 ma\u00e7\u00e3s, p\u00eassegos e bananas. O n\u00famero de ma\u00e7\u00e3s \u00e9 duplo do dos p\u00eassegos e o n\u00famero de bananas \u00e9 um ter\u00e7o do dos p\u00eassegos. Quantas s\u00e3o as pe\u00e7as&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20588,"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-6778","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-do-1--grau","tag-equacao"],"views":2571,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8V2Pag057-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6778","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=6778"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6778\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20588"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6778"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6778"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6778"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}