Answer:<\/strong> 80 gallons<\/p>\n\n\n\n Explanation (300 words)<\/strong> The prompt tells us the dishwasher needs 32 gallons to wash 4 loads, giving the ordered pair (L, W) = (4, 32). Substituting into the model lets us solve for k:<\/p>\n\n\n\n \u200332 = k \u00d7 4 So each load always requires 8 gallons. Once k is known, predicting the water for any number of loads is straightforward\u2014just multiply by 8. The question asks about 10 loads, so<\/p>\n\n\n\n \u2003W = 8 \u00d7 10 = 80.<\/p>\n\n\n\n Therefore, the dishwasher will use 80 gallons<\/strong> of water to wash 10 loads.<\/p>\n\n\n\n Why does this reasoning work? In proportional situations, doubling, tripling, or otherwise scaling one quantity scales the other by the exact same factor. If 4 loads use 32 gallons, then each load\u2019s \u201cshare\u201d of water is the constant 8 gallons. Ten loads is 2.5 times as many as four loads (because 10 \u00f7 4 = 2.5). Multiplying the original 32 gallons by 2.5 gives 32 \u00d7 2.5 = 80 gallons, matching our earlier calculation. Both the algebraic approach and the ratio-scaling approach rely on the unchanging constant value.<\/p>\n\n\n\n Recognizing direct variation is valuable in algebra because it allows us to create quick predictive models. Whether budgeting water consumption, estimating fuel costs, or converting currencies, identifying k lets you extrapolate accurately without repetitive measurement. By isolating a simple per-unit rate, you turn one recorded data point into a tool for many future reliable mathematical predictions\u2014a core idea behind linear modeling.<\/p>\n\n\n\n Classes: – Skyward – NEISD Launchpad – Select Profile Disney – Netflix – Khan Academy – Algebra Calculator – STAAR Review Direct Variation & Pythagorean Theorem – Calculator – Color Theme – Zoom 8. The amount of water an electric dishwasher uses to wash dishes varies directly with the number of loads of dishes. The […]<\/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-223815","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223815","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=223815"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223815\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Because the problem states that the amount of water used varies directly with the number of loads, the relationship is linear and passes through the origin. Mathematically, direct variation is modeled by W = kL, where W is gallons of water, L is number of loads, and k is a constant of proportionality that never changes.<\/p>\n\n\n\n
\u2003k = 32 \u00f7 4
\u2003k = 8.<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-127.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"