{"id":124644,"date":"2019-03-21T01:35:30","date_gmt":"2019-03-21T04:35:30","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=124644"},"modified":"2023-05-22T06:43:38","modified_gmt":"2023-05-22T09:43:38","slug":"probleminha-animais-em-massa","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/probleminha-animais-em-massa\/","title":{"rendered":".Probleminha: Animais em Massa"},"content":{"rendered":"<p style=\"margin:30px\">\n<div class=\"g1\" style=\"line-height:25px;\">\n<p class=\"tit\" style=\"line-height:20px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 8\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 1px; margin-bottom: 5px;border: 0 none\"\/>\n<p style=\"margin:20px\">\n<p>As figuras mostram diversas combina\u00e7\u00f5es de pesagens entre tr\u00eas animais de esp\u00e9cies distintas. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/02\/Animais-em-Massa.png\" style=\"border:none;\" alt=\"\" width=\"381\" height=\"389\" class=\"aligncenter size-full wp-image-121901\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/02\/Animais-em-Massa.png 381w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/02\/Animais-em-Massa-294x300.png 294w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Na figura [tex]4[\/tex], qual a marca correta que a balan\u00e7a deve indicar?<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1\" style=\"line-height:35px;\">\n<p class=\"tit\" style=\"line-height:20px;margin:10px\">Solu\u00e7\u00e3o 1<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 1px; margin-bottom: 2px;border: 0 none\"\/>\n<p style=\"margin:20px\">\n<p>Sejam [tex]x[\/tex] a massa do coelho, [tex]y[\/tex] a do gato e [tex]z[\/tex] a do cachorro. Podemos ent\u00e3o escrever o sistema de equa\u00e7\u00f5es:<br \/>\n[tex]\\qquad \\qquad \\begin{cases}<br \/>\nx+y=10\\\\<br \/>\nx+z=20\\\\<br \/>\ny+z=24.\\\\<br \/>\n\\end{cases}[\/tex].<br \/>\nSomando as equa\u00e7\u00f5es, obtemos [tex]2(x+y+z)=54[\/tex], donde [tex]x+y+z=27 \\, kg. [\/tex]<br \/>\nAssim, a marca correta da balan\u00e7a \u00e9 [tex] \\, \\fcolorbox{black}{#eee0e5}{$ \\, 27 \\, kg \\, $} \\, .[\/tex]<\/p>\n<p style=\"margin:20px\">\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=\"g1\" style=\"line-height:35px;\">\n<p class=\"tit\" style=\"line-height:20px;margin:10px\">Solu\u00e7\u00e3o 2<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 1px; margin-bottom: 2px;border: 0 none\"\/>\n<p style=\"margin:20px\">\n<ul>\n<li>Inicialmente, consideremos o esquema mostrado abaixo, no qual cada quadrado representa a massa de um par de animais.<\/li>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa1.png\" style=\"border:none; \"alt=\"\" width=\"297\" height=\"319\" class=\"aligncenter size-full wp-image-126556\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa1.png 297w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa1-279x300.png 279w\" sizes=\"auto, (max-width: 297px) 100vw, 297px\" \/><\/p>\n<li>Desta forma, podemos juntar tudo em um \u00fanico ret\u00e2ngulo conforme o pr\u00f3ximo desenho.<\/li>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa2.png\" style=\"border:none; \"alt=\"\" width=\"325\" height=\"282\" class=\"aligncenter size-full wp-image-126557\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa2.png 325w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa2-300x260.png 300w\" sizes=\"auto, (max-width: 325px) 100vw, 325px\" \/><\/p>\n<li>Perceba, ent\u00e3o, que temos dois animais de cada tipo nessa massa total.<\/li>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa3.png\" style=\"border:none; \"alt=\"\" width=\"328\" height=\"265\" class=\"aligncenter size-full wp-image-126558\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa3.png 328w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa3-300x242.png 300w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/p>\n<li>Agora, podemos dividir esse valor por dois para encontrarmos a massa dos tr\u00eas animais citados, em conjunto.<\/li>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa4.png\" style=\"border:none;\" alt=\"\" width=\"318\" height=\"170\" class=\"aligncenter size-full wp-image-126559\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa4.png 318w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2019\/04\/massa4-300x160.png 300w\" sizes=\"auto, (max-width: 318px) 100vw, 318px\" \/>\n<\/ul>\n<p>Logo, a massa pedida \u00e9 [tex] \\, \\fcolorbox{black}{#eee0e5}{$ \\, 27 \\, kg \\, $} \\, .[\/tex]<\/p>\n<p style=\"margin:20px\">\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>Simpatizantes da Matem\u00e1tica I<\/strong>.<\/div>\n<p style=\"margin:10px\">\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 8\u00ba ano do E. F.) As figuras mostram diversas combina\u00e7\u00f5es de pesagens entre tr\u00eas animais de esp\u00e9cies distintas. Na figura [tex]4[\/tex], qual a marca correta que a balan\u00e7a deve indicar? Solu\u00e7\u00e3o 1 Sejam [tex]x[\/tex] a massa do coelho, [tex]y[\/tex] a do gato e [tex]z[\/tex] a do cachorro. Podemos ent\u00e3o escrever &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/probleminha-animais-em-massa\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":164,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-124644","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/124644","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=124644"}],"version-history":[{"count":15,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/124644\/revisions"}],"predecessor-version":[{"id":191508,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/124644\/revisions\/191508"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=124644"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}