{"id":159567,"date":"2024-11-01T00:48:41","date_gmt":"2024-11-01T00:48:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=159567"},"modified":"2024-11-01T00:48:45","modified_gmt":"2024-11-01T00:48:45","slug":"what-two-numbers-multiply-to-189-but-add-to-66","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/01\/what-two-numbers-multiply-to-189-but-add-to-66\/","title":{"rendered":"What two numbers multiply to 189 but add to 66"},"content":{"rendered":"\n<p>What two numbers multiply to 189 but add to 66?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find two numbers that multiply to 189 and add to 66, we can denote these two numbers as ( x ) and ( y ). The problem gives us two equations based on the relationships between ( x ) and ( y ):<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>( x \\cdot y = 189 ) (the product)<\/li>\n\n\n\n<li>( x + y = 66 ) (the sum)<\/li>\n<\/ol>\n\n\n\n<p>We can start by expressing one variable in terms of the other using the sum equation. Let\u2019s solve for ( y ):<\/p>\n\n\n\n<p>[<br>y = 66 &#8211; x<br>]<\/p>\n\n\n\n<p>Next, we can substitute this expression for ( y ) into the product equation:<\/p>\n\n\n\n<p>[<br>x \\cdot (66 &#8211; x) = 189<br>]<\/p>\n\n\n\n<p>Expanding this equation gives us:<\/p>\n\n\n\n<p>[<br>66x &#8211; x^2 = 189<br>]<\/p>\n\n\n\n<p>Rearranging this into a standard quadratic equation form, we have:<\/p>\n\n\n\n<p>[<br>-x^2 + 66x &#8211; 189 = 0<br>]<\/p>\n\n\n\n<p>To make it easier to work with, we can multiply the entire equation by -1:<\/p>\n\n\n\n<p>[<br>x^2 &#8211; 66x + 189 = 0<br>]<\/p>\n\n\n\n<p>Now, we can solve this quadratic equation using the quadratic formula, which is:<\/p>\n\n\n\n<p>[<br>x = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a}<br>]<\/p>\n\n\n\n<p>In our equation, ( a = 1 ), ( b = -66 ), and ( c = 189 ). Plugging these values into the quadratic formula:<\/p>\n\n\n\n<p>[<br>x = \\frac{66 \\pm \\sqrt{(-66)^2 &#8211; 4 \\cdot 1 \\cdot 189}}{2 \\cdot 1}<br>]<\/p>\n\n\n\n<p>Calculating the discriminant:<\/p>\n\n\n\n<p>[<br>b^2 &#8211; 4ac = 4356 &#8211; 756 = 3600<br>]<\/p>\n\n\n\n<p>Taking the square root gives us:<\/p>\n\n\n\n<p>[<br>\\sqrt{3600} = 60<br>]<\/p>\n\n\n\n<p>Now we can substitute this back into the formula:<\/p>\n\n\n\n<p>[<br>x = \\frac{66 \\pm 60}{2}<br>]<\/p>\n\n\n\n<p>Calculating the two possible values for ( x ):<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>( x = \\frac{126}{2} = 63 )<\/li>\n\n\n\n<li>( x = \\frac{6}{2} = 3 )<\/li>\n<\/ol>\n\n\n\n<p>Thus, the two numbers are ( 63 ) and ( 3 ).<\/p>\n\n\n\n<p>We can verify:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Product<\/strong>: ( 63 \\times 3 = 189 )<\/li>\n\n\n\n<li><strong>Sum<\/strong>: ( 63 + 3 = 66 )<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the two numbers that multiply to 189 and add to 66 are <strong>63<\/strong> and <strong>3<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What two numbers multiply to 189 but add to 66? The Correct Answer and Explanation is: To find two numbers that multiply to 189 and add to 66, we can denote these two numbers as ( x ) and ( y ). The problem gives us two equations based on the relationships between ( x [&hellip;]<\/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-159567","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159567","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=159567"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159567\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=159567"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=159567"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=159567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}