{"id":21867,"date":"2025-06-16T07:35:15","date_gmt":"2025-06-16T07:35:15","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=21867"},"modified":"2025-06-16T07:35:19","modified_gmt":"2025-06-16T07:35:19","slug":"a-shade-of-purple-is-made-by-mixing-blue-paint-and-red-paint-in-a-53-ratio","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-shade-of-purple-is-made-by-mixing-blue-paint-and-red-paint-in-a-53-ratio\/","title":{"rendered":"A shade of purple is made by mixing blue paint and red paint in a 5:3 ratio"},"content":{"rendered":"\n<p>A shade of purple is made by mixing blue paint and red paint in a 5:3 ratio. You want to paint your kitchen with this purple and require 21 gallons to cover the whole kitchen. A. show two different ways to organize gallons of blue paint and gallons of red paint before you mix them to make an appropriate amount of the purple paint. Discuss why the color will be the same regardless of how the paint is organized.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><\/p>\n\n\n\n<p>To maintain the <strong>5:3 ratio<\/strong> of blue to red paint and make <strong>21 gallons<\/strong> of purple paint, the total number of parts in the ratio is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 (blue) + 3 (red) = <strong>8 parts<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Method 1: Use a Unit Ratio<\/h3>\n\n\n\n<p>Each part is: 21&nbsp;gallons8&nbsp;parts=2.625&nbsp;gallons&nbsp;per&nbsp;part\\frac{21\\ \\text{gallons}}{8\\ \\text{parts}} = 2.625\\ \\text{gallons per part}<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Blue paint: 5\u00d72.625=13.1255 \\times 2.625 = 13.125 gallons<\/li>\n\n\n\n<li>Red paint: 3\u00d72.625=7.8753 \\times 2.625 = 7.875 gallons<\/li>\n<\/ul>\n\n\n\n<p>So, mix <strong>13.125 gallons of blue<\/strong> with <strong>7.875 gallons of red<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Method 2: Use a Scaled Ratio<\/h3>\n\n\n\n<p>Use the ratio 5:3 scaled by a common factor.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let the multiplier be <strong>x<\/strong><\/li>\n\n\n\n<li>Then total gallons = 5x+3x=8x=215x + 3x = 8x = 21<\/li>\n\n\n\n<li>Solve: x=218=2.625x = \\frac{21}{8} = 2.625<\/li>\n<\/ul>\n\n\n\n<p>Thus, again:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Blue paint: 5\u00d72.625=13.1255 \\times 2.625 = 13.125 gallons<\/li>\n\n\n\n<li>Red paint: 3\u00d72.625=7.8753 \\times 2.625 = 7.875 gallons<\/li>\n<\/ul>\n\n\n\n<p>So again, use <strong>13.125 gallons of blue<\/strong> and <strong>7.875 gallons of red<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p>The shade of a mixed color depends on the <strong>ratio<\/strong> of the components, not their absolute amounts. In this case, the purple paint is created using a <strong>5:3 ratio<\/strong> of blue to red paint. That means for every 5 parts of blue, you must mix 3 parts of red.<\/p>\n\n\n\n<p>Whether you measure in cups, liters, or gallons, as long as the <strong>5:3 ratio is maintained<\/strong>, the final shade will remain <strong>consistent<\/strong>. The total quantity doesn\u2019t affect the color \u2014 only the <strong>proportion<\/strong> of each color does.<\/p>\n\n\n\n<p>In both methods above, we calculate how much of each paint is needed to make 21 gallons while preserving the 5:3 ratio. The <strong>first method<\/strong> uses a unit value per part, and the <strong>second method<\/strong> scales the ratio by solving algebraically. Both yield the same result: 13.125 gallons of blue and 7.875 gallons of red.<\/p>\n\n\n\n<p>If someone wanted a smaller or larger amount \u2014 say, only 10.5 gallons or 42 gallons \u2014 as long as the <strong>same 5:3 ratio<\/strong> is applied, the color would be identical. It\u2019s like following a recipe: doubling or halving ingredients maintains the flavor if the proportions are kept.<\/p>\n\n\n\n<p>Thus, the <strong>organization<\/strong> (how you calculate or scale the amounts) doesn\u2019t change the outcome \u2014 it only changes how you get there. The key is the <strong>unchanging ratio<\/strong> that defines the color.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A shade of purple is made by mixing blue paint and red paint in a 5:3 ratio. You want to paint your kitchen with this purple and require 21 gallons to cover the whole kitchen. A. show two different ways to organize gallons of blue paint and gallons of red paint before you mix them [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-21867","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21867","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=21867"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21867\/revisions"}],"predecessor-version":[{"id":21868,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21867\/revisions\/21868"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=21867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=21867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=21867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}