{"id":14730,"date":"2016-03-10T21:06:30","date_gmt":"2016-03-10T21:06:30","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=14730"},"modified":"2017-09-06T19:13:25","modified_gmt":"2017-09-06T19:13:25","slug":"math-deduction-rates-a-recursive-example","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-deduction-rates-a-recursive-example\/","title":{"rendered":"Math:  Deduction rates:  a recursive example"},"content":{"rendered":"<h1>Sometimes, deduction rates can be tricky. The tutor offers an example of a &#8220;circular argument.&#8221;<\/h1>\n<p>Let&#8217;s imagine a benevolent employer offers a health plan that costs 6% of the employee&#8217;s <em>net income<\/em>. The company&#8217;s definition of <em>net income<\/em> is gross pay minus the health plan deduction. Find the monthly health premium of an employee whose gross monthly pay is 2500.<\/p>\n<p>Solution:<\/p>\n<p>Let p be the premium amount.<\/p>\n<p>p=0.06(2500 &#8211; p)<\/p>\n<p>Expanding, we get<\/p>\n<p>p=150 &#8211; 0.06p<\/p>\n<p>Adding 0.06p to both sides, we get<\/p>\n<p>1.06p=150<\/p>\n<p>Dividing both sides by 1.06, we arrive at<\/p>\n<p>p=150\/1.06<\/p>\n<p>Finally, p=141.51<\/p>\n<p>Apparently, the health premium for a gross income of 2500 is 141.51. Let&#8217;s check:<\/p>\n<p>2500 &#8211; 141.51 = 2358.49<\/p>\n<p>If our premium is correct, it should be 6% of 2358.49:<\/p>\n<p>0.06(2358.49)=141.51<\/p>\n<p>Algebra allows for circular arguments because the same variable can occur on both sides.<\/p>\n<p>HTH:)<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sometimes, deduction rates can be tricky. The tutor offers an example of a &#8220;circular argument.&#8221; Let&#8217;s imagine a benevolent employer offers a health plan that costs 6% of the employee&#8217;s net income. The company&#8217;s definition of net income is gross &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-deduction-rates-a-recursive-example\/\"> <span class=\"screen-reader-text\">Math:  Deduction rates:  a recursive example<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[434,3],"tags":[259,1488,1489],"class_list":["post-14730","post","type-post","status-publish","format-standard","hentry","category-home-economics","category-math","tag-financial-math","tag-recursive-deduction-rate","tag-recursive-medical-plan-rate"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14730","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=14730"}],"version-history":[{"count":18,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14730\/revisions"}],"predecessor-version":[{"id":23414,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14730\/revisions\/23414"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=14730"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=14730"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=14730"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}