{"id":217831,"date":"2025-05-22T14:29:30","date_gmt":"2025-05-22T14:29:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=217831"},"modified":"2025-05-22T14:29:32","modified_gmt":"2025-05-22T14:29:32","slug":"a-company-budgeted-73000-in-total-for-project-x-and-project-y-and-the-total-actual-spending-is-exactly-as-budgeted","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/22\/a-company-budgeted-73000-in-total-for-project-x-and-project-y-and-the-total-actual-spending-is-exactly-as-budgeted\/","title":{"rendered":"A company budgeted $73000 in total for project X and project Y, and the total actual spending is exactly as budgeted."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">A company budgeted $73000 in total for project X and project Y, and the total actual spending is exactly as budgeted.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The actual spending on project X was 60% over its original budget, while project Y only used 80% of the planned budget.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Arrange the percentages of Project X and Y with budget and actual spending (in \u2018000s)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s define the budgeted amounts for <strong>Project X<\/strong> and <strong>Project Y<\/strong> as follows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let the <strong>budgeted amount for Project X be $x$<\/strong> (in \\$1,000s)<\/li>\n\n\n\n<li>Then the <strong>budgeted amount for Project Y is $73 &#8211; x$<\/strong> (since the total budget is \\$73,000 = 73 in \\$1,000s)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Use the information about actual spending<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Project X spent <strong>60% over its budget<\/strong>, so actual spending = $x + 0.6x = 1.6x$<\/li>\n\n\n\n<li>Project Y spent <strong>only 80% of its budget<\/strong>, so actual spending = $0.8(73 &#8211; x)$<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The total actual spending = \\$73,000 = 73 (in \\$1,000s), same as the total budget.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Set up the equation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>1.6x + 0.8(73 &#8211; x) = 73<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Distribute the 0.8:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>1.6x + 58.4 &#8211; 0.8x = 73<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Combine like terms:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>0.8x + 58.4 = 73<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Subtract 58.4 from both sides:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>0.8x = 14.6<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Divide by 0.8:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>x = \\frac{14.6}{0.8} = 18.25<br>$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find budget and actual spending<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Project X:<\/li>\n\n\n\n<li>Budget: <strong>\\$18,250<\/strong> \u2192 18.25 (\u2018000s)<\/li>\n\n\n\n<li>Actual: $1.6 \\times 18.25 = 29.2$ \u2192 <strong>\\$29,200<\/strong><\/li>\n\n\n\n<li>Project Y:<\/li>\n\n\n\n<li>Budget: $73 &#8211; 18.25 = 54.75$ \u2192 <strong>\\$54,750<\/strong><\/li>\n\n\n\n<li>Actual: $0.8 \\times 54.75 = 43.8$ \u2192 <strong>\\$43,800<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer (in &#8216;000s):<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Project<\/th><th>Budget (&#8216;000s)<\/th><th>Actual Spending (&#8216;000s)<\/th><th>% of Budget Used<\/th><\/tr><\/thead><tbody><tr><td>X<\/td><td>18.25<\/td><td>29.2<\/td><td>160%<\/td><\/tr><tr><td>Y<\/td><td>54.75<\/td><td>43.8<\/td><td>80%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd0d Explanation (300+ words)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In this budget allocation problem, a company planned a total budget of \\$73,000 for two projects\u2014X and Y. However, the actual expenses for these projects varied: Project X went 60% over budget, while Project Y spent only 80% of its original budget. The key constraint is that the total actual spending remained the same as the original total budget, which was \\$73,000.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve the problem, we assign a variable to the unknown budget of Project X\u2014let\u2019s call it $x$. Since the total budget is \\$73,000, the budget for Project Y becomes $73 &#8211; x$. Using the percentage changes in actual spending, we calculate that Project X\u2019s actual cost is 1.6 times its budget (due to the 60% overage), and Project Y\u2019s actual cost is 0.8 times its budget (since it used only 80% of it).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We then set up an equation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>1.6x + 0.8(73 &#8211; x) = 73<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This reflects the sum of the actual spending for both projects being equal to the total budget. Solving this equation yields $x = 18.25$, which means the budget for Project X was \\$18,250, and therefore Project Y\u2019s budget was \\$54,750.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">From here, we apply the actual spending percentages:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Project X: $1.6 \\times 18.25 = 29.2$ \u2192 \\$29,200<\/li>\n\n\n\n<li>Project Y: $0.8 \\times 54.75 = 43.8$ \u2192 \\$43,800<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Adding these two actual spending values gives the total of \\$73,000, confirming the accuracy. Finally, we organize the values into a table showing each project\u2019s budget, actual spending, and percentage of budget used. This clear breakdown ensures both numerical accuracy and conceptual understanding of budgeting variance.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-81.png\" alt=\"\" class=\"wp-image-217832\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A company budgeted $73000 in total for project X and project Y, and the total actual spending is exactly as budgeted. The actual spending on project X was 60% over its original budget, while project Y only used 80% of the planned budget. Arrange the percentages of Project X and Y with budget and actual [&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-217831","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217831","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=217831"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217831\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217831"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217831"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217831"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}