{"id":12929,"date":"2017-10-31T21:31:08","date_gmt":"2017-10-31T21:31:08","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12929"},"modified":"2022-01-16T01:48:13","modified_gmt":"2022-01-16T01:48:13","slug":"quantas-moedas-tem-o-raul","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12929","title":{"rendered":"Quantas moedas tem o Raul?"},"content":{"rendered":"<p><ul id='GTTabs_ul_12929' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12929' class='GTTabs_curr'><a  id=\"12929_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12929' ><a  id=\"12929_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_12929'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12933\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12933\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas.jpg\" data-orig-size=\"400,243\" 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=\"Moedas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas.jpg\" class=\"alignright wp-image-12933 size-medium\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas-300x182.jpg\" alt=\"\" width=\"300\" height=\"182\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas-300x182.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<\/p>\n<p>O Tom\u00e9 tem mais 30 moedas de 1 euro do que o seu amigo Raul.<\/p>\n<p>Os dois amigos juntos t\u00eam menos de 50 moedas.<\/p>\n<p>Quantas moedas tem o Raul?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12929' onClick='GTTabs_show(1,12929)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12929'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12933\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12933\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas.jpg\" data-orig-size=\"400,243\" 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=\"Moedas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas.jpg\" class=\"alignright wp-image-12933 size-medium\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas-300x182.jpg\" alt=\"\" width=\"300\" height=\"182\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas-300x182.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Euro_moedas.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>O Tom\u00e9 tem mais 30 moedas de 1 euro do que o seu amigo Raul.<\/p>\n<p>Os dois amigos juntos t\u00eam menos de 50 moedas.<\/p>\n<p>Quantas moedas tem o Raul?<\/p>\n<\/p>\n<p>Seja \\(x\\) o n\u00famero de moedas de 1 euro que o Raul tem.<br \/>\nAssim, temos:<\/p>\n<ul>\n<li>N\u00famero de moedas de 1 euro que o Tom\u00e9 tem:\u00a0\\(x + 30\\)<\/li>\n<li>Os dois amigos juntos t\u00eam menos de 50 moedas:\u00a0\\(x + \\left( {x + 30} \\right) &lt; 50\\)<\/li>\n<li>O Raul tem mais de 6 moedas:\u00a0\\(x &gt; 6\\)<\/li>\n<\/ul>\n<p>\\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{x + \\left( {x + 30} \\right) &lt; 50}\\\\{x &gt; 6}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{2x &lt; 20}\\\\{x &gt; 6}\\end{array}} \\right.}\\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x &lt; 10}\\\\{x &gt; 6}\\end{array}} \\right.}\\\\{}&amp; \\Leftrightarrow &amp;{6 &lt; x &lt; 10}\\end{array}\\]<\/p>\n<p>Portanto, o Raul tem 7, 8 ou 9 moedas de 1 euro.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12929' onClick='GTTabs_show(0,12929)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Tom\u00e9 tem mais 30 moedas de 1 euro do que o seu amigo Raul. Os dois amigos juntos t\u00eam menos de 50 moedas. Quantas moedas tem o Raul? Resolu\u00e7\u00e3o &gt;&gt;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20330,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[270],"series":[],"class_list":["post-12929","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-inequacao"],"views":2656,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/9V1Pag037-21_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12929","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=12929"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12929\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20330"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12929"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12929"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12929"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12929"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}