{"id":154971,"date":"2024-10-15T16:55:28","date_gmt":"2024-10-15T16:55:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=154971"},"modified":"2024-10-15T16:55:30","modified_gmt":"2024-10-15T16:55:30","slug":"penelope-went-to-the-store-to-buy-x-pounds-of-broccoli-for-1-10-per-pound-and-y-cans-of-soup-for-2-50-each","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/15\/penelope-went-to-the-store-to-buy-x-pounds-of-broccoli-for-1-10-per-pound-and-y-cans-of-soup-for-2-50-each\/","title":{"rendered":"Penelope went to the store to buy x pounds of broccoli for $1.10 per pound and y cans of soup for $2.50 each"},"content":{"rendered":"\n

Penelope went to the store to buy x pounds of broccoli for $1.10 per pound and y cans of soup for $2.50 each. In total, she spent less than $10. The inequality relating the purchases she made and the total purchase price is 1.10x + 2.50y < 10. Which are reasonable solutions for this situation? Check all that apply. (\u20131, 4) (0, 2) (3, 2.5) (2, 4) (0.5, 3.78) (1.5, 3)<\/p>\n\n\n\n

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

To determine which solutions are reasonable for Penelope\u2019s shopping situation, we need to analyze the inequality (1.10x + 2.50y < 10). Here, (x) represents the pounds of broccoli purchased, and (y) represents the number of cans of soup.<\/p>\n\n\n\n

First, let\u2019s rearrange the inequality:<\/p>\n\n\n\n

[
1.10x + 2.50y < 10
]<\/p>\n\n\n\n

To find valid values for (x) and (y), we can evaluate the given points to see if they satisfy this inequality:<\/p>\n\n\n\n

    \n
  1. Point (-1, 4)<\/strong>:
    [
    1.10(-1) + 2.50(4) = -1.10 + 10 = 8.90 < 10 \\quad \\text{(Valid)}
    ]<\/li>\n\n\n\n
  2. Point (0, 2)<\/strong>:
    [
    1.10(0) + 2.50(2) = 0 + 5 = 5 < 10 \\quad \\text{(Valid)}
    ]<\/li>\n\n\n\n
  3. Point (3, 2.5)<\/strong>:
    [
    1.10(3) + 2.50(2.5) = 3.30 + 6.25 = 9.55 < 10 \\quad \\text{(Valid)}
    ]<\/li>\n\n\n\n
  4. Point (2, 4)<\/strong>:
    [
    1.10(2) + 2.50(4) = 2.20 + 10 = 12.20 < 10 \\quad \\text{(Invalid)}
    ]<\/li>\n\n\n\n
  5. Point (0.5, 3.78)<\/strong>:
    [
    1.10(0.5) + 2.50(3.78) = 0.55 + 9.45 = 10.00 < 10 \\quad \\text{(Invalid)}
    ]<\/li>\n\n\n\n
  6. Point (1.5, 3)<\/strong>:
    [
    1.10(1.5) + 2.50(3) = 1.65 + 7.50 = 9.15 < 10 \\quad \\text{(Valid)}
    ]<\/li>\n<\/ol>\n\n\n\n

    Based on this evaluation, the valid solutions that satisfy the inequality (1.10x + 2.50y < 10) are:<\/p>\n\n\n\n

      \n
    • (-1, 4)<\/li>\n\n\n\n
    • (0, 2)<\/li>\n\n\n\n
    • (3, 2.5)<\/li>\n\n\n\n
    • (1.5, 3)<\/li>\n<\/ul>\n\n\n\n

      Reasoning:<\/strong><\/p>\n\n\n\n

      In the context of this problem, negative quantities of broccoli or non-integer cans of soup do not make practical sense, yet mathematically, (-1, 4) is valid. The other points represent feasible combinations of broccoli and soup that stay under the $10 limit. For instance, buying 0 pounds of broccoli and 2 cans of soup gives a total of $5, which is a reasonable purchase.<\/p>\n\n\n\n

      Understanding these calculations helps ensure Penelope stays within her budget while shopping for groceries. In real-life situations, constraints like budget, quantity limitations, and pricing can often be analyzed using such inequalities, emphasizing the importance of evaluating solutions within context.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Penelope went to the store to buy x pounds of broccoli for $1.10 per pound and y cans of soup for $2.50 each. In total, she spent less than $10. The inequality relating the purchases she made and the total purchase price is 1.10x + 2.50y < 10. Which are reasonable solutions for this situation? […]<\/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-154971","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154971","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=154971"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154971\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=154971"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=154971"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=154971"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}