Each question sandra answers incorrectly changes her overall score by -(3)\/(4) points. Sandra’s overall score was -4(1)\/(2) points, and then she answered the last question incorrectly. What was sandra’s final score?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the problem, we need to determine how many questions Sandra answered incorrectly, given that each incorrect answer changes her score by \u20133\/4<\/strong> point and her overall score is \u20134 1\/2<\/strong> points.<\/p>\n\n\n\n Sandra’s total score: Each incorrect answer deducts 3\/4 of a point. So if Sandra got x<\/em> questions wrong:<\/p>\n\n\n\n Total score = \u2013(3\/4) \u00d7 x<\/strong><\/p>\n\n\n\n We are told that the total score is \u20139\/2, so:<\/p>\n\n\n\n $$ Multiply both sides of the equation by \u20131 to remove the negative signs:<\/p>\n\n\n\n $$ Now, multiply both sides by the reciprocal<\/strong> of 3\/4 (which is 4\/3):<\/p>\n\n\n\n $$ This problem is a straightforward application of proportional reasoning using fractions. We’re told that every question Sandra gets wrong causes a deduction of 3\/4 point<\/strong>, and that the final impact on her overall score was a negative 4 1\/2 points<\/strong>. The goal is to figure out how many questions<\/strong> she must have gotten wrong to result in that total deduction.<\/p>\n\n\n\n To begin, we converted the mixed number \u20134 1\/2 into an improper fraction to make calculations easier. Mixed numbers are often tricky in algebra, so switching them into improper fractions like \u20139\/2 simplifies the equation setup.<\/p>\n\n\n\n We then wrote an algebraic expression that represents Sandra’s score deduction from incorrect answers. If she got x<\/em> questions wrong, and each one deducts 3\/4 of a point, then her total deduction is \u2013(3\/4)\u00d7x. Setting this equal to her actual total score of \u20139\/2 allows us to solve for x.<\/p>\n\n\n\n At that point, the equation \u2013(3\/4)x = \u20139\/2 is a simple linear equation. We eliminated the negatives and isolated x by multiplying by the reciprocal of 3\/4, which is 4\/3. This gives us:<\/p>\n\n\n\n $$ This tells us that Sandra must have gotten 6 questions<\/strong> wrong to end up with a score of \u20134 1\/2.<\/p>\n\n\n\n This problem is an excellent example of how understanding fraction multiplication, reciprocals, and converting between mixed and improper fractions can make solving real-world algebra problems easier.<\/p>\n","protected":false},"excerpt":{"rendered":" Each question sandra answers incorrectly changes her overall score by -(3)\/(4) points. Sandra’s overall score was -4(1)\/(2) points, and then she answered the last question incorrectly. What was sandra’s final score? The Correct Answer and Explanation is: To solve the problem, we need to determine how many questions Sandra answered incorrectly, given that each incorrect […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-213351","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213351","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=213351"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213351\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=213351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=213351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=213351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Convert the mixed number to an improper fraction<\/strong><\/h3>\n\n\n\n
\u20134 1\/2 = \u2013(4 \u00d7 2 + 1)\/2 = \u20139\/2<\/p>\n\n\n\n
\n\n\n\nStep 2: Let the number of incorrect answers be x<\/em><\/strong><\/h3>\n\n\n\n
-\\frac{3}{4}x = -\\frac{9}{2}
$$<\/p>\n\n\n\n
\n\n\n\nStep 3: Solve for x<\/strong><\/h3>\n\n\n\n
\\frac{3}{4}x = \\frac{9}{2}
$$<\/p>\n\n\n\n
x = \\frac{9}{2} \\times \\frac{4}{3} = \\frac{36}{6} = 6
$$<\/p>\n\n\n\n
\n\n\n\n\u2705 Final Answer: Sandra answered 6 questions incorrectly.<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/strong><\/h3>\n\n\n\n
x = \\frac{9}{2} \\times \\frac{4}{3} = 6
$$<\/p>\n\n\n\n