{"id":224548,"date":"2025-06-03T08:41:38","date_gmt":"2025-06-03T08:41:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224548"},"modified":"2025-06-03T08:41:40","modified_gmt":"2025-06-03T08:41:40","slug":"the-first-discount-on-a-camera-was-18","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/the-first-discount-on-a-camera-was-18\/","title":{"rendered":"The first discount on a camera was 18%"},"content":{"rendered":"\n
The first discount on a camera was 18%. The second discount was 20%. After the two discounts the price became $328. What was the original price?<\/pre>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
To find the original price<\/strong> of the camera before the two successive discounts, we work backwards from the final price of $328<\/strong>.<\/p>\n\n\n\n
\n\n\n\n
Step-by-step Solution:<\/h3>\n\n\n\n
Let the original price be x<\/strong>.<\/p>\n\n\n\n
    \n
  1. First discount<\/strong> is 18%<\/strong>, so the price after the first discount is: x\u00d7(1\u22120.18)=x\u00d70.82x \\times (1 – 0.18) = x \\times 0.82<\/li>\n\n\n\n
  2. Second discount<\/strong> is 20%<\/strong>, applied to the discounted price: (x\u00d70.82)\u00d7(1\u22120.20)=x\u00d70.82\u00d70.80(x \\times 0.82) \\times (1 – 0.20) = x \\times 0.82 \\times 0.80<\/li>\n\n\n\n
  3. The final price is given as $328<\/strong>, so: x\u00d70.82\u00d70.80=328x \\times 0.82 \\times 0.80 = 328<\/li>\n\n\n\n
  4. Simplify the multiplication: x\u00d70.656=328x \\times 0.656 = 328<\/li>\n\n\n\n
  5. Solve for x<\/strong>: x=3280.656=500x = \\frac{328}{0.656} = 500<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n
    \u2705 Correct Answer: $500<\/strong><\/h3>\n\n\n\n
    \n\n\n\n
    Explanation<\/h3>\n\n\n\n
    To determine the original price before successive discounts, it\u2019s crucial to understand how percentage reductions apply one after the other. These aren\u2019t simply additive. That is, an 18% discount followed by a 20% discount does not equal<\/strong> a 38% total discount, because the second discount is applied to a reduced price<\/strong>, not the original.<\/p>\n\n\n\n
    Start by letting the original price be x<\/strong>. After an 18% discount, you\u2019re paying 82%<\/strong> of the original price \u2014 hence, we multiply x by 0.82<\/strong>. This gives us the intermediate discounted price.<\/p>\n\n\n\n
    Next, a 20% discount is applied to this reduced price. Paying 80% of that means we multiply by 0.80<\/strong>. The cumulative effect of both discounts is therefore 0.82 \u00d7 0.80 = 0.656<\/strong>, meaning the customer ends up paying 65.6%<\/strong> of the original price.<\/p>\n\n\n\n
    We’re told that the final price after both discounts is $328<\/strong>. So we can write: 0.656\u00d7original price=3280.656 \\times \\text{original price} = 328<\/p>\n\n\n\n
    Solving for the original price involves dividing $328 by 0.656, which gives $500<\/strong>.<\/p>\n\n\n\n
    This method illustrates how percentages multiply, not add, when applied sequentially. It\u2019s a common misconception to simply add percentages, but successive percentage changes always apply to a changing base. Working backward using multiplication and division helps reverse the discounts accurately and find the original price.<\/p>\n\n\n\n
    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
    The first discount on a camera was 18%. The second discount was 20%. After the two discounts the price became $328. What was the original price? The Correct Answer and Explanation is: To find the original price of the camera before the two successive discounts, we work backwards from the final price of $328. Step-by-step […]<\/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-224548","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224548","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=224548"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224548\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224548"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224548"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224548"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}