A 31 foot board is cut in two pieces so that the longer piece is 1 foot less than three times the shorter piece<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n To solve the problem, we are given:<\/p>\n\n\n\n A 31-foot board is cut into two pieces so that the longer piece is 1 foot less than three times the shorter piece<\/strong>.<\/p>\n<\/blockquote>\n\n\n\n Let\u2019s define variables and solve it step by step.<\/p>\n\n\n\n Let the shorter piece<\/strong> be: Then the longer piece<\/strong> is: The total length of the board is 31 feet, so: x+(3x\u22121)=31x + (3x – 1) = 31<\/p>\n\n\n\n x+3x\u22121=31\u21d24x\u22121=31\u21d24x=32\u21d2x=8x + 3x – 1 = 31 \\Rightarrow 4x – 1 = 31 \\Rightarrow 4x = 32 \\Rightarrow x = 8<\/p>\n\n\n\n \u2705 Answer:<\/strong><\/p>\n\n\n\n This is a classic algebra word problem involving two parts that add up to a known total. We start by defining a variable, xx, to represent the shorter piece of the board. Since the longer piece is 1 foot less than three times the shorter, we express the longer piece as 3x\u221213x – 1.<\/p>\n\n\n\n The key insight is realizing that both pieces together must equal the total length of the board, which is 31 feet. So we create the equation x+(3x\u22121)=31x + (3x – 1) = 31, combining like terms to get 4x\u22121=314x – 1 = 31. Solving this equation by isolating xx gives us x=8x = 8, meaning the shorter piece is 8 feet long.<\/p>\n\n\n\n Substituting back, the longer piece becomes 3(8)\u22121=233(8) – 1 = 23 feet. When we add these two parts\u20148 feet and 23 feet\u2014we get 31 feet, confirming the solution is correct.<\/p>\n\n\n\n This kind of problem teaches valuable algebra skills: variable representation, equation formation from word descriptions, and basic solving techniques. It’s often used to build foundational problem-solving skills in mathematics.<\/p>\n","protected":false},"excerpt":{"rendered":" A 31 foot board is cut in two pieces so that the longer piece is 1 foot less than three times the shorter piece The correct answer and explanation is: To solve the problem, we are given: A 31-foot board is cut into two pieces so that the longer piece is 1 foot less than […]<\/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-22279","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22279","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=22279"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22279\/revisions"}],"predecessor-version":[{"id":22280,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22279\/revisions\/22280"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=22279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=22279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=22279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\n\n\n\nStep 1: Define Variables<\/strong><\/h3>\n\n\n\n
\ud83d\udc49 xx feet<\/p>\n\n\n\n
\ud83d\udc49 3x\u221213x – 1 feet (because it is 1 foot less than three times the shorter)<\/p>\n\n\n\n
\n\n\n\nStep 2: Write an Equation<\/strong><\/h3>\n\n\n\n
\n\n\n\nStep 3: Simplify and Solve<\/strong><\/h3>\n\n\n\n
\n\n\n\nStep 4: Find the Lengths<\/strong><\/h3>\n\n\n\n
\n
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\n\n\n\n300-Word Explanation<\/strong><\/h3>\n\n\n\n