{"id":211510,"date":"2025-05-04T06:19:44","date_gmt":"2025-05-04T06:19:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=211510"},"modified":"2025-05-04T06:30:30","modified_gmt":"2025-05-04T06:30:30","slug":"one-garden-had-5-times-as-many-raspberry-bushes-as-a-second-garden","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/04\/one-garden-had-5-times-as-many-raspberry-bushes-as-a-second-garden\/","title":{"rendered":"One garden had 5 times as many raspberry bushes as a second garden"},"content":{"rendered":"\n<p>One garden had 5 times as many raspberry bushes as a second garden. After 22 bushes are transplanted from the first garden to the second garden, the number of raspberry bushes in the gardens are the same. How many bushes did each garden have originally?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first garden originally had <strong>55<\/strong> raspberry bushes.<\/li>\n\n\n\n<li>The second garden originally had <strong>11<\/strong> raspberry bushes.<\/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\"><strong>Explanation (300+ words):<\/strong><\/h3>\n\n\n\n<p>Let\u2019s break this problem down step by step using algebra.<\/p>\n\n\n\n<p>We are told:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>One garden had 5 times as many raspberry bushes as a second garden.<\/p>\n<\/blockquote>\n\n\n\n<p>Let\u2019s call the number of raspberry bushes in the <strong>second garden<\/strong> <strong>x<\/strong>.<br>Then the number of raspberry bushes in the <strong>first garden<\/strong> is <strong>5x<\/strong>, since it had 5 times as many.<\/p>\n\n\n\n<p>So originally:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First garden: 5x bushes<\/li>\n\n\n\n<li>Second garden: x bushes<\/li>\n<\/ul>\n\n\n\n<p>Then, <strong>22 bushes are transplanted from the first garden to the second<\/strong>. This changes the number of bushes in both gardens:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First garden now has: 5x \u2212 22 bushes<\/li>\n\n\n\n<li>Second garden now has: x + 22 bushes<\/li>\n<\/ul>\n\n\n\n<p>According to the problem, <strong>after<\/strong> this transfer, <strong>both gardens have the same number of bushes<\/strong>.<\/p>\n\n\n\n<p>So we set up the equation: 5x\u221222=x+225x &#8211; 22 = x + 22<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Solving the equation:<\/strong><\/h3>\n\n\n\n<p>5x\u221222=x+225x &#8211; 22 = x + 22<\/p>\n\n\n\n<p>Subtract <strong>x<\/strong> from both sides: 4x\u221222=224x &#8211; 22 = 22<\/p>\n\n\n\n<p>Add <strong>22<\/strong> to both sides: 4x=444x = 44<\/p>\n\n\n\n<p>Divide both sides by 4: x=11x = 11<\/p>\n\n\n\n<p>So, the second garden originally had <strong>x = 11<\/strong> bushes.<\/p>\n\n\n\n<p>The first garden had: 5x=5\u00d711=55&nbsp;bushes5x = 5 \u00d7 11 = 55 \\text{ bushes}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Verification:<\/strong><\/h3>\n\n\n\n<p>Let\u2019s check if the final numbers are equal after transplanting 22 bushes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First garden: 55 \u2212 22 = <strong>33<\/strong> bushes<\/li>\n\n\n\n<li>Second garden: 11 + 22 = <strong>33<\/strong> bushes<\/li>\n<\/ul>\n\n\n\n<p>\u2714\ufe0f Yes, the numbers match. Both gardens end up with 33 bushes, as stated in the problem.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion:<\/strong><\/h3>\n\n\n\n<p>Originally:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First garden: <strong>55 bushes<\/strong><\/li>\n\n\n\n<li>Second garden: <strong>11 bushes<\/strong><\/li>\n<\/ul>\n\n\n\n<p>This algebraic approach ensures accuracy and logical consistency with the scenario described. Would you like a visual diagram to illustrate the transfer?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>One garden had 5 times as many raspberry bushes as a second garden. After 22 bushes are transplanted from the first garden to the second garden, the number of raspberry bushes in the gardens are the same. How many bushes did each garden have originally? The Correct Answer and Explanation is: Correct Answer: Explanation (300+ [&hellip;]<\/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-211510","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211510","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=211510"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211510\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=211510"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=211510"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=211510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}