Four gallons of water weigh 33.4 lb
How much do 7.5 gallons of water weigh?
Find the constant of variation.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the problems regarding the weight of water, we’ll address each question systematically.<\/p>\n\n\n\n First, we need to establish the weight of 1 gallon of water based on the given information. According to the problem, 4 gallons of water weigh 33.4 pounds<\/strong>. To find the weight of 1 gallon<\/strong>, we can use the following formula:<\/p>\n\n\n\n [ Now, to find the weight of 7.5 gallons<\/strong> of water, we multiply the weight of one gallon by 7.5:<\/p>\n\n\n\n [ Thus, 7.5 gallons of water weigh approximately 62.63 pounds<\/strong> (rounded to two decimal places).<\/p>\n\n\n\n The constant of variation (k) is determined by the relationship between the weight of the water and the number of gallons. The relationship is linear, meaning that the weight (W) varies directly with the number of gallons (G). The formula for direct variation is:<\/p>\n\n\n\n [ To find the constant of variation (k), we can use the values given in the problem. We already know that 4 gallons weigh 33.4 pounds<\/strong>. Plugging these values into the equation, we have:<\/p>\n\n\n\n [ Now, we can solve for k:<\/p>\n\n\n\n [ The constant of variation is 8.35 lb\/gallon<\/strong>, which indicates that for every gallon of water, it weighs 8.35 pounds.<\/p>\n\n\n\n In this scenario, we have established a direct relationship between the weight of water and the volume measured in gallons. The constant of variation represents the proportionality factor that describes how weight changes with volume.<\/p>\n\n\n\n The approach involves first finding the unit rate (weight per gallon) by dividing the total weight by the total gallons. Once the unit rate is determined, it can be used to find the weight for any given volume. This understanding is crucial in various real-life applications, such as calculating shipping weights, water consumption, and cooking measurements.<\/p>\n\n\n\n Understanding how to calculate the weight of a liquid based on its volume is also fundamental in fields like nursing, where medication dosages are often determined by weight or volume. Using consistent and accurate measurements ensures safety and efficacy in clinical settings. Overall, this problem illustrates the importance of direct variation and proportional reasoning in practical scenarios.<\/p>\n","protected":false},"excerpt":{"rendered":" Four gallons of water weigh 33.4 lbHow much do 7.5 gallons of water weigh?Find the constant of variation. The Correct Answer and Explanation is: To solve the problems regarding the weight of water, we’ll address each question systematically. a) Weight of 7.5 Gallons of Water First, we need to establish the weight of 1 gallon […]<\/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-152897","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152897","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=152897"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152897\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152897"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152897"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152897"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}a) Weight of 7.5 Gallons of Water<\/h3>\n\n\n\n
\\text{Weight of 1 gallon} = \\frac{\\text{Total weight}}{\\text{Number of gallons}} = \\frac{33.4 \\, \\text{lb}}{4 \\, \\text{gallons}} = 8.35 \\, \\text{lb\/gallon}
]<\/p>\n\n\n\n
\\text{Weight of 7.5 gallons} = 8.35 \\, \\text{lb\/gallon} \\times 7.5 \\, \\text{gallons} = 62.625 \\, \\text{lb}
]<\/p>\n\n\n\nb) Constant of Variation<\/h3>\n\n\n\n
W = k \\times G
]<\/p>\n\n\n\n
33.4 \\, \\text{lb} = k \\times 4 \\, \\text{gallons}
]<\/p>\n\n\n\n
k = \\frac{33.4 \\, \\text{lb}}{4 \\, \\text{gallons}} = 8.35 \\, \\text{lb\/gallon}
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n