{"id":35478,"date":"2025-06-24T11:10:18","date_gmt":"2025-06-24T11:10:18","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=35478"},"modified":"2025-06-24T11:10:19","modified_gmt":"2025-06-24T11:10:19","slug":"points-a-farmhouse-shelters-10-animals","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/points-a-farmhouse-shelters-10-animals\/","title":{"rendered":"points A farmhouse shelters 10 animals."},"content":{"rendered":"\n<p>points A farmhouse shelters 10 animals. Some are goats and some are ducks. Altogether there are 36 legs. How many ducks and goats are there?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, let\u2019s define:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let <strong>x<\/strong> be the number of <strong>goats<\/strong>.<\/li>\n\n\n\n<li>Let <strong>y<\/strong> be the number of <strong>ducks<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>We know two things:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The total number of animals is 10:<br><strong>x + y = 10<\/strong><\/li>\n\n\n\n<li>Goats have 4 legs and ducks have 2 legs. The total number of legs is 36:<br><strong>4x + 2y = 36<\/strong><\/li>\n<\/ol>\n\n\n\n<p>We can solve this system of equations step by step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Solve the first equation for y<\/h3>\n\n\n\n<p>From <strong>x + y = 10<\/strong>, we get:<br><strong>y = 10 &#8211; x<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Substitute into the second equation<\/h3>\n\n\n\n<p>Now plug <strong>y = 10 &#8211; x<\/strong> into the leg equation:<br><strong>4x + 2(10 &#8211; x) = 36<\/strong><br>Simplify:<br><strong>4x + 20 &#8211; 2x = 36<\/strong><br><strong>2x + 20 = 36<\/strong><br><strong>2x = 16<\/strong><br><strong>x = 8<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find y<\/h3>\n\n\n\n<p>Since <strong>x = 8<\/strong>, then <strong>y = 10 &#8211; 8 = 2<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Goats: <strong>8<\/strong><\/li>\n\n\n\n<li>Ducks: <strong>2<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This problem is a classic example of solving a system of linear equations. The scenario involves a farmhouse with 10 animals\u2014some goats and some ducks\u2014and a total of 36 legs. Each duck has 2 legs, and each goat has 4 legs. We aim to determine how many of each animal are present.<\/p>\n\n\n\n<p>We begin by letting variables represent the unknowns: x for goats and y for ducks. The first key detail tells us that there are 10 animals in total, giving us the equation x + y = 10. The second detail refers to the number of legs. Since goats have 4 legs and ducks have 2, we express the total number of legs as 4x + 2y = 36.<\/p>\n\n\n\n<p>Solving such problems often involves substitution or elimination. We isolate y in the first equation to get y = 10 &#8211; x. Then we substitute this expression into the second equation. This transforms the problem into a single-variable equation: 4x + 2(10 &#8211; x) = 36. Distributing and combining like terms simplifies the equation to 2x + 20 = 36. Subtracting 20 from both sides gives 2x = 16, and dividing by 2 yields x = 8.<\/p>\n\n\n\n<p>We then substitute x back into the first equation to find y. Since x = 8, y = 10 &#8211; 8 = 2. So, there are 8 goats and 2 ducks.<\/p>\n\n\n\n<p>We can double-check our solution: 8 goats have 32 legs, and 2 ducks have 4 legs, totaling 36 legs. This confirms our answer is accurate.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-312.jpeg\" alt=\"\" class=\"wp-image-35479\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-312.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-312-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>points A farmhouse shelters 10 animals. Some are goats and some are ducks. Altogether there are 36 legs. How many ducks and goats are there? The Correct Answer and Explanation is: To solve this problem, let\u2019s define: We know two things: We can solve this system of equations step by step. Step 1: Solve the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-35478","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35478","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=35478"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35478\/revisions"}],"predecessor-version":[{"id":35480,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35478\/revisions\/35480"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=35478"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=35478"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=35478"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}