{"id":223735,"date":"2025-06-02T09:37:37","date_gmt":"2025-06-02T09:37:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223735"},"modified":"2025-06-02T09:37:39","modified_gmt":"2025-06-02T09:37:39","slug":"linear-inequality-felix-bought-x-pounds-of-grapes-that-cost-1-25-per-pound-and-y-boxes-of-cereal-that-cost-2-50-per-box","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/linear-inequality-felix-bought-x-pounds-of-grapes-that-cost-1-25-per-pound-and-y-boxes-of-cereal-that-cost-2-50-per-box\/","title":{"rendered":"Linear Inequality Felix bought x pounds of grapes that cost $1.25 per pound and y boxes of cereal that cost $2.50 per box."},"content":{"rendered":"\n

Linear Inequality Felix bought x pounds of grapes that cost $1.25 per pound and y boxes of cereal that cost $2.50 per box. He spent less than $10. Which graph represents this scenario?
Linear Inequality Felix bought x pounds of grapes that cost
2.50 per box. He spent less than $10. Which graph represents this scenario?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

To solve the problem, let’s first turn the word problem into a mathematical inequality:<\/p>\n\n\n\n

Given:<\/h3>\n\n\n\n
    \n
  • xx: pounds of grapes at $1.25 per pound<\/li>\n\n\n\n
  • yy: boxes of cereal at $2.50 per box<\/li>\n\n\n\n
  • Felix spent less than $10<\/strong><\/li>\n<\/ul>\n\n\n\n

    Step 1: Create the inequality<\/h3>\n\n\n\n

    The total cost of grapes and cereal must be less than $10: 1.25x+2.5y<101.25x + 2.5y < 10<\/p>\n\n\n\n

    Step 2: Convert to slope-intercept form<\/h3>\n\n\n\n

    To graph it, solve for yy: 1.25x+2.5y<101.25x + 2.5y < 10<\/p>\n\n\n\n

    Subtract 1.25×1.25x from both sides: 2.5y<\u22121.25x+102.5y < -1.25x + 10<\/p>\n\n\n\n

    Divide all terms by 2.5: y<\u22120.5x+4y < -0.5x + 4<\/p>\n\n\n\n

    This is the inequality we are graphing.<\/p>\n\n\n\n

    Step 3: Analyze the Graphs<\/h3>\n\n\n\n

    We are looking for:<\/p>\n\n\n\n

      \n
    • A dashed<\/strong> line (because the inequality is strictly less than<\/strong>)<\/li>\n\n\n\n
    • A shaded region below<\/strong> the line (because it\u2019s less than<\/strong>, not greater)<\/li>\n\n\n\n
    • The line should have a slope of -0.5<\/strong> and y-intercept of 4<\/strong><\/li>\n<\/ul>\n\n\n\n

      Step 4: Identify the Correct Graph<\/h3>\n\n\n\n

      Looking at the 4 graph options:<\/p>\n\n\n\n

        \n
      • The second graph from the left<\/strong> (Graph 2) shows:\n
          \n
        • A dashed line<\/strong> (correct)<\/li>\n\n\n\n
        • Line has a negative slope<\/strong> (correct)<\/li>\n\n\n\n
        • Line crosses y-axis at 4<\/strong> (correct)<\/li>\n\n\n\n
        • Shaded below<\/strong> the line (correct)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

          \u2705 Correct Answer: The second graph from the left.<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          Final Explanation<\/h3>\n\n\n\n

          To determine the correct graph for the scenario, we begin by translating the situation into a mathematical inequality. Felix buys xx pounds of grapes at $1.25 per pound and yy boxes of cereal at $2.50 per box. Since his total spending is less than $10, we write the inequality:
          1.25x+2.5y<101.25x + 2.5y < 10
          To graph this, we rearrange it into slope-intercept form. Subtracting 1.25×1.25x from both sides and then dividing every term by 2.5 gives:
          y<\u22120.5x+4y < -0.5x + 4
          This equation tells us that the graph should have a line with slope -0.5 and y-intercept 4. Since the inequality is strictly less than (\u201c<\u201d), the line should be dashed, indicating that points on the line are not<\/strong> included in the solution. The shading should be below<\/strong> the line, representing all combinations of xx and yy where the total cost is less than<\/strong> $10.<\/p>\n\n\n\n

          By examining the four graphs, we find that the second graph from the left perfectly matches this description. It shows a dashed line with a negative slope intersecting the y-axis at 4, and the region below the line is shaded, indicating all values of xx and yy that satisfy the inequality.<\/p>\n\n\n\n

          Thus, the second graph from the left is the correct representation of the situation described.<\/p>\n\n\n\n

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

          Linear Inequality Felix bought x pounds of grapes that cost $1.25 per pound and y boxes of cereal that cost $2.50 per box. He spent less than $10. Which graph represents this scenario?Linear Inequality Felix bought x pounds of grapes that cost2.50 per box. He spent less than $10. Which graph represents this scenario? The […]<\/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-223735","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223735","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=223735"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223735\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}