{"id":222740,"date":"2025-05-31T17:18:25","date_gmt":"2025-05-31T17:18:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=222740"},"modified":"2025-05-31T17:18:27","modified_gmt":"2025-05-31T17:18:27","slug":"eula-needs-to-buy-binders-that-cost-4-each-and-notebooks-that-cost-5-each","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/31\/eula-needs-to-buy-binders-that-cost-4-each-and-notebooks-that-cost-5-each\/","title":{"rendered":"Eula needs to buy binders that cost $4 each and notebooks that cost $5 each"},"content":{"rendered":"\n

Eula needs to buy binders that cost $4 each and notebooks that cost $5 each. She has $520. The inequality 4r + 5y \u00e2\u2030\u00a4 520 represents the situation, where r represents the number of binders and y represents the number of notebooks. Step 1: Identify the x and y-intercepts of the boundary line. When r = 0, y = 104. When y = 0, r = 130. Check: None
Eula needs to buy binders that cost
5 each. She has $520. The inequality 4r + 5y \u00e2\u2030\u00a4 520 represents the situation, where r represents the number of binders and y represents the number of notebooks. Step 1: Identify the x and y-intercepts of the boundary line. When r = 0, y = 104. When y = 0, r = 130. Check: None<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Step 1: Identify the x- and y-intercepts of the boundary line.<\/strong><\/h3>\n\n\n\n

The inequality given is: 4r+5y\u22645204r + 5y \\leq 520<\/p>\n\n\n\n

This inequality represents Eula’s total spending. The boundary line<\/strong> is the equation: 4r+5y=5204r + 5y = 520<\/p>\n\n\n\n

To find the intercepts<\/strong>:<\/p>\n\n\n\n

1. y-intercept (when r = 0):<\/strong><\/h4>\n\n\n\n

Substitute r=0r = 0 into the equation: 4(0)+5y=520\u21d25y=520\u21d2y=5205=1044(0) + 5y = 520 \\Rightarrow 5y = 520 \\Rightarrow y = \\frac{520}{5} = 104<\/p>\n\n\n\n

So, the y-intercept is (0,104)(0, 104).<\/p>\n\n\n\n

2. x-intercept (when y = 0):<\/strong><\/h4>\n\n\n\n

Substitute y=0y = 0 into the equation: 4r+5(0)=520\u21d24r=520\u21d2r=5204=1304r + 5(0) = 520 \\Rightarrow 4r = 520 \\Rightarrow r = \\frac{520}{4} = 130<\/p>\n\n\n\n

So, the x-intercept is (130,0)(130, 0).<\/p>\n\n\n\n

\u2705 These values are correct:<\/strong><\/p>\n\n\n\n

    \n
  • y-intercept: (0, 104)<\/strong><\/li>\n\n\n\n
  • x-intercept: (130, 0)<\/strong><\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    \u2705 Explanation <\/strong><\/h3>\n\n\n\n

    This problem models a real-world budgeting situation using a linear inequality. Eula is deciding how many binders and notebooks to buy without exceeding a total budget of $520. Each binder costs $4 (represented by variable rr), and each notebook costs $5 (represented by variable yy). The inequality: 4r+5y\u22645204r + 5y \\leq 520<\/p>\n\n\n\n

    represents all the combinations of binders and notebooks that she can afford.<\/p>\n\n\n\n

    The boundary line 4r+5y=5204r + 5y = 520 divides the coordinate plane into two regions: one where the total cost is less than or equal to<\/strong> $520 (the feasible region), and one where it is more (which is not allowed). The intercepts help us graph this line and understand the limits.<\/p>\n\n\n\n

    The x-intercept<\/strong> tells us how many binders Eula can buy if she buys no notebooks<\/strong>\u2014this is 130 binders. The y-intercept<\/strong> tells us how many notebooks she can buy if she buys no binders<\/strong>\u2014this is 104 notebooks. Any point (r, y) that lies on or below the line<\/strong> represents a valid combination of binders and notebooks she can purchase.<\/p>\n\n\n\n

    Understanding these intercepts is crucial for visualizing the budget constraint. They define the edge of what\u2019s possible, and the area beneath the line includes all affordable combinations. By using intercepts, Eula can make informed decisions, whether she prefers more binders, more notebooks, or a mix of both\u2014while staying within budget.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Eula needs to buy binders that cost $4 each and notebooks that cost $5 each. She has $520. The inequality 4r + 5y \u00e2\u2030\u00a4 520 represents the situation, where r represents the number of binders and y represents the number of notebooks. Step 1: Identify the x and y-intercepts of the boundary line. When r […]<\/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-222740","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222740","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=222740"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222740\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=222740"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=222740"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=222740"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}