{"id":10858,"date":"2022-06-03T17:02:24","date_gmt":"2022-06-03T11:32:24","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10858"},"modified":"2022-06-03T17:02:28","modified_gmt":"2022-06-03T11:32:28","slug":"the-coach-of-a-cricket-team-buys-3-bats-and-6-balls-for-rs-3900-later-she-buys-another-bat-and-2-more-balls-of-the-same-kind-for-rs-1300","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-coach-of-a-cricket-team-buys-3-bats-and-6-balls-for-rs-3900-later-she-buys-another-bat-and-2-more-balls-of-the-same-kind-for-rs-1300\/","title":{"rendered":"The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300."},"content":{"rendered":"\n<p><strong>Question<\/strong> : The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.<\/p>\n\n\n\n<p><strong>Solution<\/strong> : Let us denote the set of one bat by Rs x and one ball by Rs y. Then, the algebraic representation is given by the following equations :<\/p>\n\n\n\n<p>3x + 6y = 3900                      &#8230;&#8230;.(1)<\/p>\n\n\n\n<p>and  x + 2y = 1300                 &#8230;..(2)<\/p>\n\n\n\n<p>To obtain the equivalent geometric representation, we find two points on the line representing each equation. That is, we find two solutions of each equation.<\/p>\n\n\n\n<p>These solutions are given below in the table.<\/p>\n\n\n\n<p>For 3x + 6y = 3900<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>x<\/td><td>0<\/td><td>1300<\/td><\/tr><tr><td>y<\/td><td>650<\/td><td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>For x + 2y = 1300<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>x<\/td><td>500<\/td><td>100<\/td><\/tr><tr><td>y<\/td><td>400<\/td><td>600<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>We plot the points A(0, 650) and B(1300, 0) to obtain the geometric representation of 3x + 6y = 3900 and C(500, 400) and D(100, 600) to obtain the geometric representations of x + 2y = 1300.<\/p>\n\n\n\n<p>We observe that these lines are <strong>coincident.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-medium is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-1-2.jpeg?fit=300%2C197&amp;ssl=1\" alt=\"\" class=\"wp-image-10861\" width=\"398\" height=\"262\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-1-2.jpeg?w=1700&amp;ssl=1 1700w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-1-2.jpeg?resize=300%2C197&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-1-2.jpeg?resize=1024%2C674&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-1-2.jpeg?resize=768%2C506&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/06\/linearequation3-1-2.jpeg?resize=1536%2C1011&amp;ssl=1 1536w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Question : The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically. Solution : Let us denote the set of one bat by Rs x and one ball &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/the-coach-of-a-cricket-team-buys-3-bats-and-6-balls-for-rs-3900-later-she-buys-another-bat-and-2-more-balls-of-the-same-kind-for-rs-1300\/\"> <span class=\"screen-reader-text\">The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[911,43],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. 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