{"id":25843,"date":"2023-05-21T10:36:59","date_gmt":"2023-05-21T09:36:59","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25843"},"modified":"2023-05-21T12:25:18","modified_gmt":"2023-05-21T11:25:18","slug":"o-mealheiro-da-rita","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25843","title":{"rendered":"O mealheiro da Rita"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25843' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25843' class='GTTabs_curr'><a  id=\"25843_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25843' ><a  id=\"25843_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_25843'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A Rita tem 5,50 euros no mealheiro. No total, tem 17 moedas, sendo umas de 20 c\u00eantimos e outras de 50 c\u00eantimos.<br \/>Seja <em>x<\/em> o n\u00famero de moedas de 20 c\u00eantimos e seja <em>y<\/em> o n\u00famero de moedas de 50 c\u00eantimos que a Rita tem no mealheiro.<\/p>\n<ol>\n<li>Indica qual dos sistemas seguintes permite determinar quantas moedas de 20 c\u00eantimos e quantas moedas de 50 c\u00eantimos tem a Rita no mealheiro.<br \/>\\[\\begin{array}{*{20}{l}}{{\\rm{(A)}}\\;\\;\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 17}\\\\{\\begin{array}{*{20}{l}}{20x + 50y = 55}\\end{array}}\\end{array}} \\right.}&amp;{}&amp;{{\\rm{(B)}}\\;\\;\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 17}\\\\{\\begin{array}{*{20}{l}}{0,2x + 0,5y = 5,5}\\end{array}}\\end{array}} \\right.}\\\\{{\\rm{(C)}}\\;\\;\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 55}\\\\{\\begin{array}{*{20}{l}}{20x + 50y = 17}\\end{array}}\\end{array}} \\right.}&amp;{}&amp;{{\\rm{(D)}}\\;\\;\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 5,5}\\\\{\\begin{array}{*{20}{l}}{0,2x + 0,5y = 17}\\end{array}}\\end{array}} \\right.}\\end{array}\\]<\/li>\n<li>Quantas moedas de cada tipo tem a Rita no mealheiro?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25843' onClick='GTTabs_show(1,25843)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25843'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A Rita tem 5,50 euros no mealheiro. No total, tem 17 moedas, sendo umas de 20 c\u00eantimos e outras de 50 c\u00eantimos. Seja <em>x<\/em> o n\u00famero de moedas de 20 c\u00eantimos e seja <em>y<\/em> o n\u00famero de moedas de 50 c\u00eantimos que a Rita tem no mealheiro.<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>Indica qual dos sistemas seguintes permite determinar quantas moedas de 20 c\u00eantimos e quantas moedas de 50 c\u00eantimos tem a Rita no mealheiro.\\[\\begin{array}{*{20}{l}}{{\\rm{(A)}}\\;\\;\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 17}\\\\{\\begin{array}{*{20}{l}}{20x + 50y = 55}\\end{array}}\\end{array}} \\right.}&amp;{}&amp;{{\\rm{(B)}}\\;\\;\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 17}\\\\{\\begin{array}{*{20}{l}}{0,2x + 0,5y = 5,5}\\end{array}}\\end{array}} \\right.}\\\\{{\\rm{(C)}}\\;\\;\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 55}\\\\{\\begin{array}{*{20}{l}}{20x + 50y = 17}\\end{array}}\\end{array}} \\right.}&amp;{}&amp;{{\\rm{(D)}}\\;\\;\\left\\{ {\\begin{array}{*{20}{l}}{x + y = 5,5}\\\\{\\begin{array}{*{20}{l}}{0,2x + 0,5y = 17}\\end{array}}\\end{array}} \\right.}\\end{array}\\]<\/blockquote>\n<\/li>\n<li>\n<blockquote>Quantas moedas de cada tipo tem a Rita no mealheiro?<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>\u00c9 o sistema (B) que permite determinar quantas moedas de 20 c\u00eantimos e quantas moedas de 50 c\u00eantimos tem a Rita no mealheiro.<br \/><br \/><\/li>\n<li>Passemos a resolver o sistema (B):<br \/><br \/>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%; background-color: #ede664;\"><strong>1.\u00aa equa\u00e7\u00e3o<\/strong><\/td>\n<td style=\"width: 50%; background-color: #ede664;\"><strong>2.\u00aa equa\u00e7\u00e3o<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; background-color: #ede664;\"><strong>\\({x + y = 17}\\)<\/strong><\/td>\n<td style=\"width: 50%; background-color: #ede664;\"><strong>\\({0,2x + 0,5y = 5,5}\\)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\\(\\begin{array}{*{20}{c}}{x + y = 17}&amp; \\Leftrightarrow &amp;{x = 17 &#8211; y}\\end{array}\\)<\/td>\n<td style=\"width: 50%;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\u00a0<\/td>\n<td style=\"width: 50%;\">\\(\\begin{array}{*{20}{l}}{0,2\\left( {17 &#8211; y} \\right) + 0,5y = 5,5}&amp; \\Leftrightarrow &amp;{3,4 &#8211; 0,2y + 0,5y = 5,5}\\\\{}&amp; \\Leftrightarrow &amp;{0,3y = 2,1}\\\\{}&amp; \\Leftrightarrow &amp;{y = 7}\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\\(\\begin{array}{*{20}{c}}{x = 17 &#8211; 7}&amp; \\Leftrightarrow &amp;{x = 10}\\end{array}\\)<\/td>\n<td style=\"width: 50%;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\" colspan=\"2\">Solu\u00e7\u00e3o do sistema: \\(\\left( {10,7} \\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<br \/>Portanto, a Rita tem 10 moedas de 20 c\u00eantimos e 7 moedas de 50 c\u00eantimos, no mealheiro.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25843' onClick='GTTabs_show(0,25843)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A Rita tem 5,50 euros no mealheiro. No total, tem 17 moedas, sendo umas de 20 c\u00eantimos e outras de 50 c\u00eantimos.Seja x o n\u00famero de moedas de 20 c\u00eantimos e&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19188,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,345,344,239],"series":[],"class_list":["post-25843","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-grafico","tag-sistema-de-equacoes"],"views":83,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat74.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25843","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=25843"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25843\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19188"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25843"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25843"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25843"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25843"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}