{"id":4151,"date":"2024-11-02T13:56:56","date_gmt":"2024-11-02T17:56:56","guid":{"rendered":"https:\/\/josmfs.net\/?p=4151"},"modified":"2024-11-09T12:59:00","modified_gmt":"2024-11-09T17:59:00","slug":"tricky-ratio-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2024\/11\/02\/tricky-ratio-puzzle\/","title":{"rendered":"Tricky Ratio Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4148\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/11\/Tricky-Ratio-Fig2.jpg\" alt=\"\" width=\"250\" height=\"150\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/11\/Tricky-Ratio-Fig2.jpg 498w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/11\/Tricky-Ratio-Fig2-300x180.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/>This is an interesting algebra <a href=\"https:\/\/medium.com\/bellas-weekly-math-games\/an-algebra-challenge-0a0123be470c\">problem<\/a> from <em>BL\u2019s Weekly Math Games<\/em>, which is behind a subscription wall.<\/p>\n<p style=\"text-align: center;\">(<em>a<\/em><sup>3<\/sup> \u2013 <em>b<\/em><sup>3<\/sup>)\/(<em>a \u2013 b<\/em>)<sup>3<\/sup> = 73\/3,<\/p>\n<p>what is <em>a \u2013 b<\/em>?\u201d<\/p>\n<p>In fact, it is possible to solve for <em>a<\/em> and <em>b<\/em> individually as well.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/11\/Tricky-Ratio-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See a <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/11\/Tricky-Ratio-Puzzle-241027.pdf\">Tricky Ratio Puzzle<\/a> for the solution.<\/p>\n<p><strong>(Updates 11\/6\/2024, 11\/9\/2024) \u00a0Other Solutions<\/strong><!--more--><\/p>\n<p><strong>(Update 11\/6\/2024) \u00a0BL\u2019s Solution<\/strong><\/p>\n<p>Rummaging around I found the beginnings of BL\u2019s <a href=\"https:\/\/medium.com\/bellas-weekly-math-games\/an-algebra-challenge-c4dec24375ee\">solution<\/a>, again because I am not a subscriber.\u00a0 I added the remaining steps as I imagined them.\u00a0 His solution is simpler.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/11\/Tricky-Ratio-Puzzle-BL-Soln.pdf\">BL\u2019s Solution<\/a><\/p>\n<p><strong>(Update 11\/9\/2024) \u00a0Oscar Roja\u2019s Solution<\/strong><\/p>\n<p>Oscar Rojas has a different take on a solution.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/11\/Tricky-Ratio-Puzzle-Oscar-Soln.pdf\">Oscar Rojas\u2019s Solution<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is an interesting algebra problem from BL\u2019s Weekly Math Games, which is behind a subscription wall. (a3 \u2013 b3)\/(a \u2013 b)3 = 73\/3, what is a \u2013 b?\u201d In fact, it is possible to solve for a and b individually as well. Answer. See a Tricky Ratio Puzzle for the solution. (Updates 11\/6\/2024, 11\/9\/2024) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[133,274],"class_list":["post-4151","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-algebra","tag-bl-puzzles"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4151","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=4151"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4151\/revisions"}],"predecessor-version":[{"id":4171,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4151\/revisions\/4171"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}