{"id":9682,"date":"2024-11-08T13:33:56","date_gmt":"2024-11-08T13:33:56","guid":{"rendered":"https:\/\/mathsweekengland.co.uk\/?p=9682"},"modified":"2024-11-08T13:34:36","modified_gmt":"2024-11-08T13:34:36","slug":"ks3-solutions","status":"publish","type":"post","link":"https:\/\/mathsweekengland.co.uk\/?p=9682","title":{"rendered":"KS3 Solutions"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"9682\" class=\"elementor elementor-9682\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-790c56ba e-flex e-con-boxed e-con e-parent\" data-id=\"790c56ba\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-62b11eaf e-con-full e-flex e-con e-child\" data-id=\"62b11eaf\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-52420061 elementor-widget elementor-widget-heading\" data-id=\"52420061\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">2024 Daily Puzzles - Key Stage 3 Solutions<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6330898 elementor-widget elementor-widget-image\" data-id=\"6330898\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"768\" height=\"768\" src=\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3-768x768.png\" class=\"attachment-medium_large size-medium_large wp-image-9690\" alt=\"Monday: A + B + B + C + A + C = 11 + 19 + 16. Rearrange and 2A + 2B + 2C = 46. So A + B + C = 23 but if B + C = 19 then A must be 4. Now substitute into A + C = 16 and C = 12. Tuesday: P is 3 and Q is 4 therefore P x Q = 12 Wednesday: 144 cm. Let its body be y, its tail will then be 18cm + 1\/2 y. But y = 18cm + 18cm + 1\/2y. So 1\/2y = 36cm. Double both sides: y = 72cm. Now add all together: body 72cm + head 18cm + tail 54cm = 144cm Thursday: Guess and check. The correct number must have been in the 50s. 5 cannot be taken away from Bella&apos;s 55 or added to Ann&apos;s 50, as this would have given one of the incorrect answers, so it must come off Cindy&apos;s 58, giving 53. Friday: 30 minutes\" srcset=\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3-768x768.png 768w, https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3-300x300.png 300w, https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3-1024x1024.png 1024w, https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3-150x150.png 150w, https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3.png 1080w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>KS3 Solutions<\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_cbd_carousel_blocks":"[]","footnotes":""},"categories":[50,67,72,62,38],"tags":[],"class_list":["post-9682","post","type-post","status-publish","format-standard","hentry","category-50","category-2024-daily-puzzles","category-ks3-2024-daily-puzzles","category-ks3","category-primary"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>KS3 Solutions - Maths Week England<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathsweekengland.co.uk\/?p=9682\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KS3 Solutions - Maths Week England\" \/>\n<meta property=\"og:description\" content=\"KS3 Solutions\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathsweekengland.co.uk\/?p=9682\" \/>\n<meta property=\"og:site_name\" content=\"Maths Week England\" \/>\n<meta property=\"article:published_time\" content=\"2024-11-08T13:33:56+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-11-08T13:34:36+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1080\" \/>\n\t<meta property=\"og:image:height\" content=\"1080\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Sam Hartburn\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Sam Hartburn\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9682#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9682\"},\"author\":{\"name\":\"Sam Hartburn\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/550ba1223e711011fb8439ae5c6df22b\"},\"headline\":\"KS3 Solutions\",\"datePublished\":\"2024-11-08T13:33:56+00:00\",\"dateModified\":\"2024-11-08T13:34:36+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9682\"},\"wordCount\":8,\"publisher\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/#organization\"},\"image\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9682#primaryimage\"},\"thumbnailUrl\":\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3-768x768.png\",\"articleSection\":[\"2024\",\"2024 Daily Puzzles\",\"KS3\",\"KS3\",\"Primary\"],\"inLanguage\":\"en-GB\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9682\",\"url\":\"https:\/\/mathsweekengland.co.uk\/?p=9682\",\"name\":\"KS3 Solutions - 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Rearrange and 2A + 2B + 2C = 46. So A + B + C = 23 but if B + C = 19 then A must be 4. Now substitute into A + C = 16 and C = 12. Tuesday: P is 3 and Q is 4 therefore P x Q = 12 Wednesday: 144 cm. Let its body be y, its tail will then be 18cm + 1\/2 y. But y = 18cm + 18cm + 1\/2y. So 1\/2y = 36cm. Double both sides: y = 72cm. Now add all together: body 72cm + head 18cm + tail 54cm = 144cm Thursday: Guess and check. The correct number must have been in the 50s. 5 cannot be taken away from Bella's 55 or added to Ann's 50, as this would have given one of the incorrect answers, so it must come off Cindy's 58, giving 53. Friday: 30 minutes\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/?p=9682#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathsweekengland.co.uk\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"KS3 Solutions\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#website\",\"url\":\"https:\/\/mathsweekengland.co.uk\/\",\"name\":\"Maths Week England\",\"description\":\"11th - 17th November 2024\",\"publisher\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathsweekengland.co.uk\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-GB\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#organization\",\"name\":\"Maths Week England\",\"url\":\"https:\/\/mathsweekengland.co.uk\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2023\/09\/MWElogo.png\",\"contentUrl\":\"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2023\/09\/MWElogo.png\",\"width\":1602,\"height\":946,\"caption\":\"Maths Week England\"},\"image\":{\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/550ba1223e711011fb8439ae5c6df22b\",\"name\":\"Sam Hartburn\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/3e5422498c5d12df034b3437aea5b9998e45961ff6bf2db93ba2bfb566798119?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/3e5422498c5d12df034b3437aea5b9998e45961ff6bf2db93ba2bfb566798119?s=96&d=mm&r=g\",\"caption\":\"Sam Hartburn\"},\"url\":\"https:\/\/mathsweekengland.co.uk\/?author=11\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"KS3 Solutions - 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Maths Week England","isPartOf":{"@id":"https:\/\/mathsweekengland.co.uk\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mathsweekengland.co.uk\/?p=9682#primaryimage"},"image":{"@id":"https:\/\/mathsweekengland.co.uk\/?p=9682#primaryimage"},"thumbnailUrl":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3-768x768.png","datePublished":"2024-11-08T13:33:56+00:00","dateModified":"2024-11-08T13:34:36+00:00","breadcrumb":{"@id":"https:\/\/mathsweekengland.co.uk\/?p=9682#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathsweekengland.co.uk\/?p=9682"]}]},{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/mathsweekengland.co.uk\/?p=9682#primaryimage","url":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3.png","contentUrl":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2024\/11\/Solutions-KS3.png","width":1080,"height":1080,"caption":"Monday: A + B + B + C + A + C = 11 + 19 + 16. Rearrange and 2A + 2B + 2C = 46. So A + B + C = 23 but if B + C = 19 then A must be 4. Now substitute into A + C = 16 and C = 12. Tuesday: P is 3 and Q is 4 therefore P x Q = 12 Wednesday: 144 cm. Let its body be y, its tail will then be 18cm + 1\/2 y. But y = 18cm + 18cm + 1\/2y. So 1\/2y = 36cm. Double both sides: y = 72cm. Now add all together: body 72cm + head 18cm + tail 54cm = 144cm Thursday: Guess and check. The correct number must have been in the 50s. 5 cannot be taken away from Bella's 55 or added to Ann's 50, as this would have given one of the incorrect answers, so it must come off Cindy's 58, giving 53. Friday: 30 minutes"},{"@type":"BreadcrumbList","@id":"https:\/\/mathsweekengland.co.uk\/?p=9682#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathsweekengland.co.uk\/"},{"@type":"ListItem","position":2,"name":"KS3 Solutions"}]},{"@type":"WebSite","@id":"https:\/\/mathsweekengland.co.uk\/#website","url":"https:\/\/mathsweekengland.co.uk\/","name":"Maths Week England","description":"11th - 17th November 2024","publisher":{"@id":"https:\/\/mathsweekengland.co.uk\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathsweekengland.co.uk\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-GB"},{"@type":"Organization","@id":"https:\/\/mathsweekengland.co.uk\/#organization","name":"Maths Week England","url":"https:\/\/mathsweekengland.co.uk\/","logo":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/mathsweekengland.co.uk\/#\/schema\/logo\/image\/","url":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2023\/09\/MWElogo.png","contentUrl":"https:\/\/mathsweekengland.co.uk\/wp-content\/uploads\/2023\/09\/MWElogo.png","width":1602,"height":946,"caption":"Maths Week England"},"image":{"@id":"https:\/\/mathsweekengland.co.uk\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/550ba1223e711011fb8439ae5c6df22b","name":"Sam Hartburn","image":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/mathsweekengland.co.uk\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/3e5422498c5d12df034b3437aea5b9998e45961ff6bf2db93ba2bfb566798119?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/3e5422498c5d12df034b3437aea5b9998e45961ff6bf2db93ba2bfb566798119?s=96&d=mm&r=g","caption":"Sam Hartburn"},"url":"https:\/\/mathsweekengland.co.uk\/?author=11"}]}},"_links":{"self":[{"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/posts\/9682","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9682"}],"version-history":[{"count":4,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/posts\/9682\/revisions"}],"predecessor-version":[{"id":9693,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=\/wp\/v2\/posts\/9682\/revisions\/9693"}],"wp:attachment":[{"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9682"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathsweekengland.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}