{"id":430,"date":"2012-09-20T21:09:12","date_gmt":"2012-09-20T21:09:12","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=430"},"modified":"2018-02-22T21:21:33","modified_gmt":"2018-02-22T21:21:33","slug":"inequalities-phone-plans","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/inequalities-phone-plans\/","title":{"rendered":"Inequalities: Phone Plans"},"content":{"rendered":"

Which phone plan to choose?\u00a0 A little math tutoring can help you\u00a0decide.<\/h1>\n

Let’s assume we have two choices:<\/p>\n\n\n\n\n
Plan A<\/td>\n$12 per month<\/td>\n$0.10 per text<\/td>\n<\/tr>\n
Plan B<\/td>\n$18 per month<\/td>\n$0.07 per text<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

How do you decide which plan to use?<\/p>\n

Let’s say you’re buying the plan for a month.\u00a0 Let x be the number of texts you send.\u00a0 Then your cost is<\/p>\n

$12 + $0.10x for Plan A<\/p>\n

$18 + $0.07x for Plan B<\/p>\n

You pay more up front with\u00a0Plan B, but its texts\u00a0are cheaper.\u00a0 There will be\u00a0a specific number of texts at which the plans cost the\u00a0same:<\/p>\n

12 + 0.10x =18 + 0.07x<\/p>\n

Using algebra, we solve for x:<\/p>\n

    \n
  1. Subtract 0.07x from both sides to get\n

    12 + 0.03x = 18<\/li>\n

  2. Subtract 12 from from both sides:\n

    0.03x=6<\/li>\n

  3. Divide both sides by 0.03:\n

    x=200<\/li>\n<\/ol>\n

    At 200 texts, the two plans are equal in price for one month.\u00a0 Any more texts, and Plan B must be cheaper:\u00a0 it’s less per text.<\/p>\n

    Now, let’s explore the situation from the point of view of inequalities.\u00a0 We ask, “For what number of texts will Plan B be cheaper?”<\/p>\n

    18 + 0.07x ≤ 12 + 0.10x<\/p>\n

      \n
    1. Subtract 18 from both sides\n

      0.07x ≤ -6 + 0.10x<\/li>\n

    2. Subtract 0.10x from both sides\n

      -0.03x ≤ -6<\/li>\n

    3. Divide both sides by -0.03: you must flip the sign when doing so<\/b>:\n

      x ≥ 200<\/li>\n<\/ol>\n

      Note that algebraic operations are the same<\/strong> for inequalities as for equations, with one important exception:\u00a0 you must flip the sign if you divide or multiply by a negative number.<\/strong>\u00a0 (Not by positive, just by negative).<\/p>\n

      The two methods make the same conclusion, but from different points of view.\u00a0 The equation tells us that, at 200 texts, the two plans cost the same.\u00a0 The inequality, on the other hand, tells us that if we\u00a0make more than\u00a0200\u00a0texts, we’ll pay less with Plan B.<\/p>\n

      Jack of Oracle Tutoring by Jack and Diane<\/a>, Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Which phone plan to choose?\u00a0 A little math tutoring can help you\u00a0decide. Let’s assume we have two choices: Plan A $12 per month $0.10 per text Plan B $18 per month $0.07 per text How do you decide which plan …<\/p>\n

      Inequalities: Phone Plans<\/span> Read More »<\/a><\/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":[2760,2758,2759],"class_list":["post-430","post","type-post","status-publish","format-standard","hentry","category-math","tag-how-to-find-if-one-phone-plan-is-better","tag-rules-about-inequalities","tag-when-to-flip-the-sign-of-an-inequality"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/430","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=430"}],"version-history":[{"count":56,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/430\/revisions"}],"predecessor-version":[{"id":30317,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/430\/revisions\/30317"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=430"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=430"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=430"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}