{"id":43562,"date":"2025-06-30T08:17:06","date_gmt":"2025-06-30T08:17:06","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=43562"},"modified":"2025-06-30T08:17:07","modified_gmt":"2025-06-30T08:17:07","slug":"how-many-pairs-of-whole-numbers-numbers-have-a-sum-of-40","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/how-many-pairs-of-whole-numbers-numbers-have-a-sum-of-40\/","title":{"rendered":"How many pairs of whole numbers numbers have a sum of 40"},"content":{"rendered":"\n<p>How many pairs of whole numbers numbers have a sum of 40<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine how many pairs of whole numbers have a sum of 40, you need to find all pairs of non-negative integers (a, b) that satisfy the equation: a+b=40a + b = 40<\/p>\n\n\n\n<p>where both aa and bb are whole numbers (non-negative integers).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step explanation:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Range of values for aa:<\/strong> Since a+b=40a + b = 40, aa must be a whole number between 0 and 40 (inclusive). If a=0a = 0, then b=40b = 40. If a=1a = 1, then b=39b = 39, and so on. The largest possible value for aa is 40, where b=0b = 0.<\/li>\n\n\n\n<li><strong>Counting the pairs:<\/strong> For each possible value of aa, there is exactly one corresponding value of bb. Specifically, b=40\u2212ab = 40 &#8211; a. Therefore, for a=0,1,2,\u2026,40a = 0, 1, 2, \\dots, 40, the corresponding values of bb are 40,39,38,\u2026,040, 39, 38, \\dots, 0.<\/li>\n\n\n\n<li><strong>Conclusion:<\/strong> The possible values for aa are 0 through 40, inclusive, giving a total of 41 different values for aa. Each value of aa corresponds to a unique pair (a,b)(a, b). Therefore, the number of pairs of whole numbers that sum to 40 is:<\/li>\n<\/ol>\n\n\n\n<p>41\\boxed{41}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This problem is a simple counting problem where you are asked to determine how many different ways you can pair two non-negative integers that sum to 40. Since the relationship between aa and bb is linear (i.e., b=40\u2212ab = 40 &#8211; a), and both aa and bb are bounded between 0 and 40, the number of solutions corresponds directly to the number of possible values for aa, which are 41 in total.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How many pairs of whole numbers numbers have a sum of 40 The correct answer and explanation is: To determine how many pairs of whole numbers have a sum of 40, you need to find all pairs of non-negative integers (a, b) that satisfy the equation: a+b=40a + b = 40 where both aa and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-43562","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43562","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=43562"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43562\/revisions"}],"predecessor-version":[{"id":43563,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43562\/revisions\/43563"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=43562"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=43562"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=43562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}