{"id":11456,"date":"2024-10-05T17:28:32","date_gmt":"2024-10-05T17:28:32","guid":{"rendered":"https:\/\/findpath.xyz\/?p=11456"},"modified":"2024-10-05T17:28:32","modified_gmt":"2024-10-05T17:28:32","slug":"solve-this-mathematical-hard-quiz","status":"publish","type":"post","link":"https:\/\/findpath.xyz\/?p=11456","title":{"rendered":"Solve this mathematical hard quiz !"},"content":{"rendered":"<p>To solve this problem step by step, we need to carefully analyze the equations given and work out the values of the variables\u00a0<span class=\"katex\"><span class=\"katex-mathml\">AA<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span>,\u00a0<span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><\/span><\/span><\/span>, and\u00a0<span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span>, then apply them to find the value of\u00a0<span class=\"katex\"><span class=\"katex-mathml\">A+B\u00d7CA + B \\times C<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span>.<\/p><div class=\"311fe198f191a864c1efcdfa9efedfdf\" data-index=\"3\" style=\"float: none; margin:0px 0 0px 0; text-align:center;\">\n<div data-type=\"_mgwidget\" data-widget-id=\"1782571\">\r\n<\/div>\r\n<script>(function(w,q){w[q]=w[q]||[];w[q].push([\"_mgc.load\"])})(window,\"_mgq\");\r\n<\/script>\r\n\n<\/div>\n\n<h3>Step 1: Solve for\u00a0<span class=\"katex\"><span class=\"katex-mathml\">AA<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/h3>\n<p>We start with the first equation:<\/p>\n<div class=\"code-block code-block-3\"><\/div>\n<div class=\"code-block code-block-3\"><\/div>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A+A=20A + A = 20<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>This simplifies to:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">2A=202A = 20<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span><\/p>\n<div class=\"code-block code-block-4\"><\/div>\n<p>By dividing both sides by 2:<\/p>\n<div class=\"code-block code-block-4\"><\/div>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A=10A = 10<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>Step 2: Solve for\u00a0<span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><\/span><\/span><\/span><\/h3>\n<p>Next, we move to the second equation:<\/p>\n<div class=\"code-block code-block-5\"><\/div>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">B+B=10B + B = 10<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>This simplifies to:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">2B=102B = 10<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>By dividing both sides by 2:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">B=5B = 5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>Step 3: Solve for\u00a0<span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span><\/h3>\n<p>Now, we solve for\u00a0<span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span>\u00a0using the third equation:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">C+C=8C + C = 8<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>This simplifies to:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">2C=82C = 8<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>By dividing both sides by 2:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">C=4C = 4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>Step 4: Apply the values to the final equation<\/h3>\n<p>Now that we have the values for\u00a0<span class=\"katex\"><span class=\"katex-mathml\">AA<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span>,\u00a0<span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><\/span><\/span><\/span>, and\u00a0<span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span>, we can substitute them into the final equation\u00a0<span class=\"katex\"><span class=\"katex-mathml\">A+B\u00d7CA + B \\times C<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span>:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A+B\u00d7CA + B \\times C<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Using the values\u00a0<span class=\"katex\"><span class=\"katex-mathml\">A=10A = 10<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><\/span><\/span><\/span>,\u00a0<span class=\"katex\"><span class=\"katex-mathml\">B=5B = 5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span>, and\u00a0<span class=\"katex\"><span class=\"katex-mathml\">C=4C = 4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span>:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">10+5\u00d7410 + 5 \\times 4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">10<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>According to the order of operations (PEMDAS\/BODMAS), multiplication comes before addition, so we first multiply:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">5\u00d74=205 \\times 4 = 20<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Now we add:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">10+20=3010 + 20 = 30<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">10<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">20<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">30<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>Final Answer:<\/h3>\n<p>The solution to\u00a0<span class=\"katex\"><span class=\"katex-mathml\">A+B\u00d7CA + B \\times C<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span>\u00a0is:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">3030<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">30<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>Explanation Summary:<\/h3>\n<ol>\n<li><span class=\"katex\"><span class=\"katex-mathml\">AA<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span>\u00a0is found by solving\u00a0<span class=\"katex\"><span class=\"katex-mathml\">A+A=20A + A = 20<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">20<\/span><\/span><\/span><\/span>, resulting in\u00a0<span class=\"katex\"><span class=\"katex-mathml\">A=10A = 10<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><\/span><\/span><\/span>.<\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\">BB<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><\/span><\/span><\/span>\u00a0is found by solving\u00a0<span class=\"katex\"><span class=\"katex-mathml\">B+B=10B + B = 10<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><\/span><\/span><\/span>, resulting in\u00a0<span class=\"katex\"><span class=\"katex-mathml\">B=5B = 5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span>.<\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span>\u00a0is found by solving\u00a0<span class=\"katex\"><span class=\"katex-mathml\">C+C=8C + C = 8<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><\/span><\/span><\/span>, resulting in\u00a0<span class=\"katex\"><span class=\"katex-mathml\">C=4C = 4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span>.<\/li>\n<li>Substituting these values into\u00a0<span class=\"katex\"><span class=\"katex-mathml\">A+B\u00d7CA + B \\times C<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span>\u00a0and applying the order of operations leads to the final answer of 30.<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n\n<div style=\"font-size: 0px; height: 0px; line-height: 0px; margin: 0; padding: 0; clear: both;\"><\/div>","protected":false},"excerpt":{"rendered":"<p>To solve this problem step by step, we need to carefully analyze the equations given and work out the values of the variables\u00a0AAA,\u00a0BBB, and\u00a0CCC, then apply them&#8230; <\/p>\n","protected":false},"author":1,"featured_media":11457,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-11456","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/findpath.xyz\/index.php?rest_route=\/wp\/v2\/posts\/11456","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/findpath.xyz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/findpath.xyz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/findpath.xyz\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/findpath.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11456"}],"version-history":[{"count":1,"href":"https:\/\/findpath.xyz\/index.php?rest_route=\/wp\/v2\/posts\/11456\/revisions"}],"predecessor-version":[{"id":11458,"href":"https:\/\/findpath.xyz\/index.php?rest_route=\/wp\/v2\/posts\/11456\/revisions\/11458"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/findpath.xyz\/index.php?rest_route=\/wp\/v2\/media\/11457"}],"wp:attachment":[{"href":"https:\/\/findpath.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11456"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/findpath.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11456"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/findpath.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}