At the snack bar, hot dogs cost $4 each and bottled water costs $2 each. In the first business hour of the day, less than $12 worth of hot dogs and water were sold. Which are reasonable solutions for this situation if x represents the number of hot dogs sold and y represents the number of bottles of water sold? Check all that apply. (\u20131, 5) (0, 6) (2, 1) (1, 1.5) (1, 3) (2, 2)<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine which of the given pairs ((x, y)) are reasonable solutions for the sales of hot dogs and bottled water, we start by defining the problem mathematically. Let (x) represent the number of hot dogs sold and (y) represent the number of bottles of water sold. The cost of hot dogs is $4 each, and the cost of bottled water is $2 each. The total sales can be represented by the inequality:<\/p>\n\n\n\n [ This inequality indicates that the total revenue from selling hot dogs and bottled water must be less than $12.<\/p>\n\n\n\n Now, we will evaluate each of the provided points:<\/p>\n\n\n\n Based on this evaluation, the reasonable solutions that satisfy the inequality (4x + 2y < 12) are:<\/p>\n\n\n\n In conclusion, only (2, 1), (1, 1.5), and (1, 3) meet the criteria for sales, ensuring that the total revenue remains under $12, while (0, 6) and (2, 2) do not comply, and (-1, 5) is not feasible due to negative hot dog sales.<\/p>\n","protected":false},"excerpt":{"rendered":" At the snack bar, hot dogs cost $4 each and bottled water costs $2 each. In the first business hour of the day, less than $12 worth of hot dogs and water were sold. Which are reasonable solutions for this situation if x represents the number of hot dogs sold and y represents the number […]<\/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-145551","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145551","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=145551"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145551\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=145551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=145551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=145551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
4x + 2y < 12
]<\/p>\n\n\n\n\n
[
4(-1) + 2(5) = -4 + 10 = 6 < 12
]
This point is a reasonable solution; however, selling negative hot dogs is not feasible.<\/li>\n\n\n\n
[
4(0) + 2(6) = 0 + 12 = 12
]
This does not satisfy the condition since it equals $12, not less than $12.<\/li>\n\n\n\n
[
4(2) + 2(1) = 8 + 2 = 10 < 12
]
This is a valid solution.<\/li>\n\n\n\n
[
4(1) + 2(1.5) = 4 + 3 = 7 < 12
]
This is a valid solution.<\/li>\n\n\n\n
[
4(1) + 2(3) = 4 + 6 = 10 < 12
]
This is a valid solution.<\/li>\n\n\n\n
[
4(2) + 2(2) = 8 + 4 = 12
]
This does not satisfy the inequality since it equals $12, not less than $12.<\/li>\n<\/ol>\n\n\n\n\n