{"id":224128,"date":"2025-06-02T17:55:32","date_gmt":"2025-06-02T17:55:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224128"},"modified":"2025-06-02T17:55:34","modified_gmt":"2025-06-02T17:55:34","slug":"at-a-tennis-match-the-snack-bar-sells-hot-dogs-for-4-dollars-and-slices-of-pizza-for-5-dollars","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/at-a-tennis-match-the-snack-bar-sells-hot-dogs-for-4-dollars-and-slices-of-pizza-for-5-dollars\/","title":{"rendered":"At a tennis match the snack bar sells hot dogs for 4 dollars and slices of pizza for 5 dollars"},"content":{"rendered":"\n

At a tennis match the snack bar sells hot dogs for 4 dollars and slices of pizza for 5 dollars. The snack bar sold 49 hot dogs and slices of pizza all together for $221 dollars. Part A: Enter the total number of hot dogs sold. Part B: Enter the total number of slices of pizza sold.<\/p>\n\n\n\n

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

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

Part A (hot dogs): 24<\/strong>
Part B (pizza slices): 25<\/strong><\/p>\n\n\n\n

\n\n\n\n

Why those numbers work <\/h3>\n\n\n\n

Whenever you see a problem that gives you two totals<\/strong>\u2014one for quantity<\/em> (how many items) and one for cost<\/em> (how much money)\u2014it is almost always solved cleanly by setting up a system of two linear equations<\/strong>. Think of the two unknowns we need:<\/p>\n\n\n\n

    \n
  • hh = number of hot dogs sold<\/li>\n\n\n\n
  • pp = number of pizza slices sold<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    1. Build the \u201chow many\u201d equation<\/h4>\n\n\n\n

    The statement \u201csold 49 hot dogs and slices of pizza<\/strong> altogether\u201d<\/em> tells us the combined count is 49. In symbols: h+p=49.h + p = 49.<\/p>\n\n\n\n

    This captures the physical<\/em> total\u2014literally how many individual items left the snack bar.<\/p>\n\n\n\n

    \n\n\n\n

    2. Build the \u201chow much money\u201d equation<\/h4>\n\n\n\n

    Each hot dog brings in $4; each pizza slice brings in $5. Multiplying the price by the quantity of each item and then adding gives the total revenue<\/strong> of $221: 4h+5p=221.4h + 5p = 221.<\/p>\n\n\n\n

    \n\n\n\n

    3. Solve the system<\/h4>\n\n\n\n

    There are many ways\u2014substitution, elimination, or matrices. Substitution is quick here.<\/p>\n\n\n\n

    From the first equation: p=49\u2212h.p = 49 – h.<\/p>\n\n\n\n

    Plug that expression for pp into the money equation: 4h+5(49\u2212h)=221.4h + 5(49 – h) = 221.<\/p>\n\n\n\n

    Distribute and combine like terms: 4h+245\u22125h=221\u21d2\u2212h+245=221\u21d2\u2212h=\u221224\u21d2h=24.4h + 245 – 5h = 221 \\Rightarrow -h + 245 = 221 \\Rightarrow -h = -24 \\Rightarrow h = 24.<\/p>\n\n\n\n

    So 24 hot dogs<\/strong> were sold.<\/p>\n\n\n\n

    Use hh to find pp: p=49\u2212h=49\u221224=25.p = 49 – h = 49 – 24 = 25.<\/p>\n\n\n\n

    So 25 pizza slices<\/strong> were sold.<\/p>\n\n\n\n

    \n\n\n\n

    4. Reasonableness check<\/h4>\n\n\n\n
      \n
    • Quantities are whole numbers (makes sense for individual items).<\/li>\n\n\n\n
    • Prices are realistic multiples: 24\u00d7$4=$9624 \\times \\$4 = \\$96 and 25\u00d7$5=$12525 \\times \\$5 = \\$125.<\/li>\n\n\n\n
    • Adding the money confirms the total: $96 + $125 = $221.<\/li>\n\n\n\n
    • Adding the items confirms the count: 24 + 25 = 49.<\/li>\n<\/ul>\n\n\n\n

      Both checks pass, so the numbers are consistent with every fact given in the problem.<\/p>\n\n\n\n

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

      At a tennis match the snack bar sells hot dogs for 4 dollars and slices of pizza for 5 dollars. The snack bar sold 49 hot dogs and slices of pizza all together for $221 dollars. Part A: Enter the total number of hot dogs sold. Part B: Enter the total number of slices of […]<\/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-224128","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224128","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=224128"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224128\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}