{"id":6442,"date":"2013-11-22T00:15:07","date_gmt":"2013-11-22T00:15:07","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6442"},"modified":"2014-12-02T08:26:55","modified_gmt":"2014-12-02T08:26:55","slug":"more-problem-solving-strategies-working-backwards","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/11\/22\/more-problem-solving-strategies-working-backwards\/","title":{"rendered":"More Problem-Solving Strategies: Working Backwards"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Working backwards is another way to solve some math problems.\u00a0 If the result is given at the end of a series, follow each step until the problem is complete.\u00a0 Then check each step to make sure each one is correct.<\/p>\n

What Facts Are Known?<\/strong><\/p>\n

As in all math problems, read the problem very carefully to determine what is known.\u00a0 For example, suppose the problem is, “Robert spent one-fifth of his money buying a paperback book, then half of what was left for a haircut.\u00a0 Then he bought lunch for $7.\u00a0 When he got home, he had $13 left.\u00a0 How much did he have originally?”\u00a0 What is known is the final amount, every operation, and each step along the way.<\/p>\n

What Are the Steps?<\/strong><\/p>\n

The first step in working backwards is to take the final number and then do the inverse operation. Therefore, is a step involves subtraction, the inverse will be addition, and if it involves division the inverse will be multiplication.\u00a0 Read the problem once again to determine each step. \u00a0In this problem, \u00a0the first backwards step will be to add an amount, \u00a0and the second will be to multiply.\u00a0 The last step will to be to multiply again, then divide.<\/p>\n

What Is the Solution?<\/strong><\/p>\n

In this example, if a-7 = 13, then add 7 to each side, so that a -7 +7 = 13+7 , or a = 20.\u00a0 Robert had 20 dollars before he bought lunch.\u00a0 If he spent half of what was left in the next step, the inverse operation is used again, so that (1\/2b)2 = 20(2), or 40 dollars before the haircut.\u00a0 Read very carefully for the last step, as one fifth of the money is one fifth of the total amount, rather than one-fifth of what is left.\u00a0 That means that 40 dollars is only 4\/5 of the total.\u00a0 Therefore, if 4\/5 of c = 40 , 4c= 200.\u00a0 Then c =50.\u00a0 The original amount is 50 dollars.<\/p>\n

Checking the Solution<\/strong><\/p>\n

To check the solution, follow the steps forward.\u00a0 If Robert had 50 dollars originally, then a 10-dollar paperback would be one-fifth of the total, because 10 is 1\/5 of 50.\u00a0 There was 40 dollars before the haircut, and half of what was left is $20.\u00a0 Then 20-7 is 13 dollars so the steps check.\u00a0 Sometimes, working backwards is a good strategy to solve problems.<\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Greenwich, CT visit: Tutoring in Greenwich, CT<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview: Working backwards is another way to solve some math problems.\u00a0 If the result is given at the end of a series, follow each step until the problem is complete.\u00a0 Then check each step to make sure each one is correct. What Facts Are Known? As in all math problems, read the problem very carefully […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[971,1391,2584],"class_list":["post-6442","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-inverse-operations","tag-problem-solving","tag-working-backwards"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6442","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6442"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6442\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6442"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6442"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6442"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}