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 solve the problem regarding Eula’s purchasing situation, we begin by establishing the variables and the inequality representing her constraints. Let ( x ) represent the number of binders and ( y ) represent the number of notebooks she wants to buy. The costs associated with these items lead us to the inequality:<\/p>\n\n\n\n [ If Eula decides to purchase 7 notebooks, we need to substitute ( y = 7 ) back into the inequality to find out how many binders she can still buy:<\/p>\n\n\n\n [ Since ( x ) must be a whole number, the greatest number of binders Eula can buy in this scenario is 1 binder<\/strong>.<\/p>\n\n\n\n In summary, Eula can buy a maximum of 5 binders or 10 notebooks. If she buys 7 notebooks, she can afford to purchase only 1 binder. This analysis highlights the constraints imposed by her budget, allowing her to make informed purchasing decisions while adhering to her financial limitations. The graph of the inequality ( 4x + 2y \\leq 20 ) visually represents the feasible combinations of binders and notebooks Eula can afford within her budget.<\/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-145095","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145095","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=145095"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145095\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=145095"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=145095"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=145095"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
4x + 2y \\leq 20
]<\/p>\n\n\n\nFinding Maximum Binders and Notebooks<\/h3>\n\n\n\n
\n
To determine the maximum number of binders ( x ) that Eula can buy, we set ( y = 0 ) in the inequality: [
4x + 2(0) \\leq 20 \\implies 4x \\leq 20 \\implies x \\leq 5
] Hence, the greatest number of binders Eula can buy is 5 binders<\/strong>.<\/li>\n\n\n\n
Similarly, to find the maximum number of notebooks ( y ) she can buy, we set ( x = 0 ): [
4(0) + 2y \\leq 20 \\implies 2y \\leq 20 \\implies y \\leq 10
] Therefore, the greatest number of notebooks Eula can buy is 10 notebooks<\/strong>.<\/li>\n<\/ol>\n\n\n\nBinders with 7 Notebooks<\/h3>\n\n\n\n
4x + 2(7) \\leq 20 \\implies 4x + 14 \\leq 20 \\implies 4x \\leq 6 \\implies x \\leq 1.5
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n