{"id":36208,"date":"2015-05-01T20:36:33","date_gmt":"2015-05-01T23:36:33","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=36208"},"modified":"2023-03-21T22:03:29","modified_gmt":"2023-03-22T01:03:29","slug":"probleminha-misturando-tudo","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/probleminha-misturando-tudo\/","title":{"rendered":".Probleminha: Misturando tudo"},"content":{"rendered":"<p style=\"margin:10px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 7\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n(<strong>Olimp\u00edada de Minas Gerais<\/strong>-2004) Uma mistura do tipo [tex]I[\/tex] cont\u00e9m suco de lim\u00e3o, \u00f3leo e vinagre na propor\u00e7\u00e3o [tex]1:2:3[\/tex].<br \/>\nNuma segunda mistura, do tipo [tex]II[\/tex], a propor\u00e7\u00e3o \u00e9 [tex]3:4:5[\/tex].<br \/>\nQual \u00e9 a propor\u00e7\u00e3o de suco de lim\u00e3o, \u00f3leo e vinagre numa mistura composta de [tex]1[\/tex] litro da mistura do tipo [tex]I[\/tex] e [tex]1[\/tex] litro da mistura do tipo [tex]II[\/tex]?\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 30px;border: 0 none\"\/>\n<ul>\n<li>Consideremos a mistura [tex]I[\/tex]:<br \/>\na propor\u00e7\u00e3o [tex]1:2:3[\/tex] significa que em [tex]1[\/tex] litro teremos [tex]\\dfrac{1}{6}[\/tex] litro de suco de lim\u00e3o, [tex]\\dfrac{2}{6}[\/tex] litro de \u00f3leo e [tex]\\dfrac{3}{6}[\/tex] litro de vinagre. <\/li>\n<li>J\u00e1 na mistura [tex]II[\/tex], a propor\u00e7\u00e3o \u00e9 [tex]3:4:5[\/tex].<br \/>\nPortanto, em [tex]1[\/tex] litro teremos [tex]\\dfrac{3}{12}[\/tex] litro de suco de lim\u00e3o, [tex]\\dfrac{4}{12}[\/tex] litro de \u00f3leo e [tex]\\dfrac{5}{12}[\/tex] litro de vinagre.<\/li>\n<\/ul>\n<p> Ao juntarmos [tex]1[\/tex] litro de [tex]I[\/tex] e [tex]1[\/tex] litro de [tex]II[\/tex], teremos:<\/p>\n<p style=\"margin:20px\">\n<p>[tex]\\qquad \\dfrac{1}{6}+\\dfrac{3}{12}=\\dfrac{5}{12}[\/tex] litro de suco de lim\u00e3o; <\/p>\n<p style=\"margin:20px\">\n<p>[tex]\\qquad \\dfrac{2}{6}+\\dfrac{4}{12}=\\dfrac{8}{12}[\/tex] litro de \u00f3leo; <\/p>\n<p style=\"margin:20px\">\n<p>[tex]\\qquad \\dfrac {3}{6}+\\dfrac{5}{12}=\\dfrac{11}{12}[\/tex] litro de vinagre. <\/p>\n<p style=\"margin:10px\">\n<p>Como agora temos [tex]2[\/tex] litros de mistura, ent\u00e3o: <\/p>\n<p style=\"margin:20px\">\n<p>[tex]\\qquad \\dfrac{\\dfrac{5}{12}}{2}=\\dfrac{5}{24}[\/tex] \u00e9 a fra\u00e7\u00e3o de suco de lim\u00e3o;<\/p>\n<p style=\"margin:20px\">\n<p>[tex]\\qquad \\dfrac{\\dfrac{8}{12}}{2}=\\dfrac{8}{24}[\/tex] \u00e9 a fra\u00e7\u00e3o de \u00f3leo;<\/p>\n<p style=\"margin:20px\">\n<p>[tex]\\qquad \\dfrac{\\dfrac{11}{12}}{2}=\\dfrac{11}{24}[\/tex] \u00e9 a fra\u00e7\u00e3o de vinagre na mistura. <\/p>\n<p style=\"margin:10px\">\n<p><strong>Portanto, a propor\u00e7\u00e3o final da mistura \u00e9 [tex]5:8:11[\/tex].<\/strong><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelos <strong> Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g3\">\nParticipou da discuss\u00e3o o Clube <strong>KH\u00c9RIMA<\/strong>.<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 7\u00ba ano do E. F.) (Olimp\u00edada de Minas Gerais-2004) Uma mistura do tipo [tex]I[\/tex] cont\u00e9m suco de lim\u00e3o, \u00f3leo e vinagre na propor\u00e7\u00e3o [tex]1:2:3[\/tex]. Numa segunda mistura, do tipo [tex]II[\/tex], a propor\u00e7\u00e3o \u00e9 [tex]3:4:5[\/tex]. Qual \u00e9 a propor\u00e7\u00e3o de suco de lim\u00e3o, \u00f3leo e vinagre numa mistura composta de [tex]1[\/tex] &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/probleminha-misturando-tudo\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":164,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-36208","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/36208","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/164"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=36208"}],"version-history":[{"count":27,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/36208\/revisions"}],"predecessor-version":[{"id":185092,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/36208\/revisions\/185092"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=36208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}