{"id":26190,"date":"2023-06-04T22:10:10","date_gmt":"2023-06-04T21:10:10","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26190"},"modified":"2023-06-04T22:34:56","modified_gmt":"2023-06-04T21:34:56","slug":"os-cromos-da-joana-e-da-maria","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26190","title":{"rendered":"Os cromos da Joana e da Maria"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26190' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26190' class='GTTabs_curr'><a  id=\"26190_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26190' ><a  id=\"26190_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_26190'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A Joana e a Maria t\u00eam, juntas, 360 cromos.<br \/>Se a Joana der 40 cromos \u00e0 Maria, elas ficam com igual n\u00famero de cromos.<br \/>O n\u00famero de cromos da Joana \u00e9:<\/p>\n<p><strong>[A]<\/strong> 140\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> 160\u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 200\u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> 220<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26190' onClick='GTTabs_show(1,26190)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26190'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A Joana e a Maria t\u00eam, juntas, 360 cromos.<br \/>Se a Joana der 40 cromos \u00e0 Maria, elas ficam com igual n\u00famero de cromos.<br \/>O n\u00famero de cromos da Joana \u00e9:<\/p>\n<p><strong>[A]<\/strong> 140\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> 160\u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 200\u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> 220<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>Como a Joana tem maior n\u00famero de cromos do que a Maria, ent\u00e3o podemos eliminar as duas primeiras op\u00e7\u00f5es.<\/p>\n<p>A op\u00e7\u00e3o <strong>[C]<\/strong> tamb\u00e9m \u00e9 desadequada, pois se a Joana desse 40 dos seus 200 cromos \u00e0 Maria, esta ficaria com cromos do que ela.<\/p>\n<p>Resta, por isso, a op\u00e7\u00e3o <strong>[D]<\/strong> 220, que passaremos a validar.<br \/>Se a joana tivesse 220 cromos, ent\u00e3o a Maria teria 140 cromos. Assim, dando a Joana \u00e0 Maria 40 dos seus cromos, ambas ficariam com 180 cromos.<\/p>\n<p>\u00a0<\/p>\n<h6>Uma alternativa mais laboriosa<\/h6>\n<p>Designemos por <em>j<\/em> e por <em>m<\/em>, respetivamente, o n\u00famero de cromos da Joana e o n\u00famero de cromos da Maria.<\/p>\n<p>Equacionando o problemas e resolvendo o sistema de equa\u00e7\u00f5es, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{j + m = 360}\\\\{j &#8211; 40 = m + 40}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{j = 360 &#8211; m}\\\\{360 &#8211; m &#8211; 40 = m + 40}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{m = 140}\\\\{j = 220}\\end{array}} \\right.}\\end{array}\\]<\/p>\n<p>Portanto, a Joana tem 220 cromos.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26190' onClick='GTTabs_show(0,26190)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A Joana e a Maria t\u00eam, juntas, 360 cromos.Se a Joana der 40 cromos \u00e0 Maria, elas ficam com igual n\u00famero de cromos.O n\u00famero de cromos da Joana \u00e9: [A] 140\u00a0&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19176,"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-26190","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":107,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat67.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26190","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=26190"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26190\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19176"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26190"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26190"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26190"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}