{"id":179871,"date":"2025-01-02T18:02:42","date_gmt":"2025-01-02T18:02:42","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=179871"},"modified":"2025-01-02T18:02:44","modified_gmt":"2025-01-02T18:02:44","slug":"a-radio-station-is-giving-away-tickets","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/02\/a-radio-station-is-giving-away-tickets\/","title":{"rendered":"A radio station is giving away tickets"},"content":{"rendered":"\n<p>A radio station is giving away tickets. To play. They plan to give away tickets for seats that cost 10$ and 20$. They want to give away at least 20 tickets. The total cost of the tickets cannot exceed $280. A radio station is giving away tickets. To play. They plan to give away tickets for seats that cost 10$ and 20$. They want to give away at least 20 tickets. The total cost of the tickets cannot exceed $280.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>Let&#8217;s solve this problem step by step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Problem Breakdown:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The radio station is giving away tickets for seats that cost $10 and $20.<\/li>\n\n\n\n<li>They want to give away at least 20 tickets.<\/li>\n\n\n\n<li>The total cost of the tickets cannot exceed $280.<\/li>\n<\/ul>\n\n\n\n<p>We need to figure out how many $10 tickets (let&#8217;s call this ( x )) and $20 tickets (let&#8217;s call this ( y )) satisfy the conditions:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The total number of tickets must be at least 20:<br>[<br>x + y \\geq 20<br>]<\/li>\n\n\n\n<li>The total cost of the tickets cannot exceed $280:<br>[<br>10x + 20y \\leq 280<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Simplifying the Cost Condition<\/h3>\n\n\n\n<p>We can simplify the cost inequality by dividing it by 10:<br>[<br>x + 2y \\leq 28<br>]<\/p>\n\n\n\n<p>Now we have two inequalities:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>( x + y \\geq 20 )<\/li>\n\n\n\n<li>( x + 2y \\leq 28 )<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve the System of Inequalities<\/h3>\n\n\n\n<p>We now need to find values of ( x ) and ( y ) that satisfy both inequalities.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Express ( x ) in terms of ( y ):<\/h4>\n\n\n\n<p>From the first inequality ( x + y \\geq 20 ), solve for ( x ):<br>[<br>x \\geq 20 &#8211; y<br>]<\/p>\n\n\n\n<p>Substitute this into the second inequality ( x + 2y \\leq 28 ):<br>[<br>(20 &#8211; y) + 2y \\leq 28<br>]<br>Simplify:<br>[<br>20 + y \\leq 28<br>]<br>[<br>y \\leq 8<br>]<\/p>\n\n\n\n<p>So, the value of ( y ) (the number of $20 tickets) can range from 0 to 8.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 3: Determine the Number of $10 Tickets<\/h4>\n\n\n\n<p>Now, using ( y \\leq 8 ), we find the corresponding values for ( x ).<\/p>\n\n\n\n<p>For ( y = 8 ), substitute into ( x + y \\geq 20 ):<br>[<br>x + 8 \\geq 20 \\implies x \\geq 12<br>]<br>Thus, when ( y = 8 ), ( x ) must be at least 12. The total cost will be:<br>[<br>10(12) + 20(8) = 120 + 160 = 280<br>]<br>This satisfies both conditions.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Conclusion:<\/h4>\n\n\n\n<p>The radio station can give away:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>12 $10 tickets<\/strong> and <strong>8 $20 tickets<\/strong>.<br>This satisfies the total ticket condition (at least 20 tickets) and the total cost condition (not exceeding $280).<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>A radio station is giving away tickets. To play. They plan to give away tickets for seats that cost 10$ and 20$. They want to give away at least 20 tickets. The total cost of the tickets cannot exceed $280. A radio station is giving away tickets. To play. They plan to give away tickets [&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-179871","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179871","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=179871"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179871\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179871"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179871"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}