Eula needs to buy binders that cost $4 each and notebooks that cost $2 each. She has $20. The graph of the inequality 4x + 2y \u2264 20, which represents the situation, is shown. What is the greatest number of binders Eula can buy? What is the greatest number of notebooks Eula can buy? If Eula buys 7 notebooks, what is the greatest number of binders she can buy?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine how many binders (x) and notebooks (y) Eula can buy with her $20 budget, we start with the inequality representing her spending:<\/p>\n\n\n\n [ Step 1: Analyzing the Inequality<\/strong><\/p>\n\n\n\n Step 2: Finding Maximum Quantities of Binders and Notebooks<\/strong><\/p>\n\n\n\n Step 3: If Eula Buys 7 Notebooks<\/strong><\/p>\n\n\n\n Now, if Eula decides to buy 7 notebooks, we can substitute (y = 7) into the inequality to find how many binders she can still buy:<\/p>\n\n\n\n [ [ Since Eula can only buy a whole number of binders, she can buy at most 1 binder<\/strong> if she purchases 7 notebooks.<\/p>\n\n\n\n Summary<\/strong>:<\/p>\n\n\n\n This analysis shows the relationship between Eula’s budget and her purchasing options for binders and notebooks, helping her make informed decisions based on her needs.<\/p>\n","protected":false},"excerpt":{"rendered":" Eula needs to buy binders that cost $4 each and notebooks that cost $2 each. She has $20. The graph of the inequality 4x + 2y \u2264 20, which represents the situation, is shown. What is the greatest number of binders Eula can buy? What is the greatest number of notebooks Eula can buy? If […]<\/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-145510","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145510","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=145510"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145510\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=145510"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=145510"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=145510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
4x + 2y \\leq 20
]<\/p>\n\n\n\n\n
\n
\n
The inequality states that the total cost of binders and notebooks cannot exceed $20.<\/li>\n<\/ol>\n\n\n\n\n
To find the maximum number of binders Eula can buy when she spends all her money on binders, set (y = 0):
[
4x \\leq 20 \\implies x \\leq 5
]
Therefore, the greatest number of binders Eula can buy is 5 binders<\/strong>.<\/li>\n\n\n\n
To find the maximum number of notebooks she can buy when she spends all her money on notebooks, set (x = 0):
[
2y \\leq 20 \\implies y \\leq 10
]
Thus, the greatest number of notebooks Eula can buy is 10 notebooks<\/strong>.<\/li>\n<\/ol>\n\n\n\n
4x + 2(7) \\leq 20 \\implies 4x + 14 \\leq 20
]
Subtract 14 from both sides:<\/p>\n\n\n\n
4x \\leq 6 \\implies x \\leq \\frac{6}{4} = 1.5
]<\/p>\n\n\n\n\n