{"id":26037,"date":"2023-05-24T22:36:23","date_gmt":"2023-05-24T21:36:23","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26037"},"modified":"2023-05-24T22:58:19","modified_gmt":"2023-05-24T21:58:19","slug":"uma-conversa-sobre-cromos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26037","title":{"rendered":"Uma conversa sobre cromos"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26037' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26037' class='GTTabs_curr'><a  id=\"26037_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26037' ><a  id=\"26037_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_26037'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O Alberto disse \u00e0 Teresa: &#8220;Se tu me deres \\( \\ldots \\) cromos, ficarei com tantos como tu.&#8221;<br \/>A Teresa replicou: &#8220;Se eu te der \\( \\ldots \\) cromos, tu ficar\u00e1s com o \\( \\ldots \\) dos meus.&#8221;<\/p>\n<ol>\n<li>A Marta, que ouviu a conversa, traduziu esta situa\u00e7\u00e3o atrav\u00e9s do seguinte sistema de equa\u00e7\u00f5es: \\[\\left\\{ {\\begin{array}{*{20}{l}}{a + 6 = t &#8211; 6}\\\\{a + 10 = 2\\left( {t &#8211; 10} \\right)}\\end{array}} \\right.\\] Copia e completa a conversa entre os dois amigos, tendo em aten\u00e7\u00e3o o sistema que a Marta escreveu.<br \/><br \/><\/li>\n<li>Quantos cromos tem cada um dos amigos?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26037' onClick='GTTabs_show(1,26037)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26037'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>O Alberto disse \u00e0 Teresa: &#8220;Se tu me deres \\( \\ldots \\) cromos, ficarei com tantos como tu.&#8221;<br \/>A Teresa replicou: &#8220;Se eu te der \\( \\ldots \\) cromos, tu ficar\u00e1s com o \\( \\ldots \\) dos meus.&#8221;<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>A Marta, que ouviu a conversa, traduziu esta situa\u00e7\u00e3o atrav\u00e9s do seguinte sistema de equa\u00e7\u00f5es: \\[\\left\\{ {\\begin{array}{*{20}{l}}{a + 6 = t &#8211; 6}\\\\{a + 10 = 2\\left( {t &#8211; 10} \\right)}\\end{array}} \\right.\\] Copia e completa a conversa entre os dois amigos, tendo em aten\u00e7\u00e3o o sistema que a Marta escreveu.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Quantos cromos tem cada um dos amigos?<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>O Alberto disse \u00e0 Teresa: &#8220;Se tu me deres <span style=\"color: #0000ff;\">\\(6\\)<\/span> cromos, ficarei com tantos como tu.&#8221;<br \/>A Teresa replicou: &#8220;Se eu te der <span style=\"color: #0000ff;\">\\(10\\)<\/span> cromos, tu ficar\u00e1s com o <span style=\"color: #0000ff;\">dobro<\/span> dos meus.&#8221;<br \/><br \/><\/li>\n<li>Resolvendo o sistema, temos: \\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{a + 6 = t &#8211; 6}\\\\{a + 10 = 2\\left( {t &#8211; 10} \\right)}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{a = t &#8211; 12}\\\\{t &#8211; 12 + 10 = 2t &#8211; 20}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{a = t &#8211; 12}\\\\{ &#8211; t = &#8211; 18}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{a = t &#8211; 12}\\\\{t = 18}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{a = 6}\\\\{t = 18}\\end{array}} \\right.}&amp;{}\\\\{}&amp;{}&amp;{}&amp;{}&amp;{S = \\left\\{ {\\left( {6,18} \\right)} \\right\\}}&amp;{}\\end{array}\\] O Alberto tem 6 cromos e a Teresa tem 18 cromos.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26037' onClick='GTTabs_show(0,26037)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Alberto disse \u00e0 Teresa: &#8220;Se tu me deres \\( \\ldots \\) cromos, ficarei com tantos como tu.&#8221;A Teresa replicou: &#8220;Se eu te der \\( \\ldots \\) cromos, tu ficar\u00e1s com&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14083,"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-26037","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":75,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26037","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=26037"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26037\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26037"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26037"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26037"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26037"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}