The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The given problem states that the value of ( y ) varies directly with ( x ). This means that there is a constant ratio between ( y ) and ( x ). The relationship can be written as:<\/p>\n\n\n\n [ where ( k ) is the constant of proportionality.<\/p>\n\n\n\n We are given that when ( x = 3 ), ( y = 21 ). To find ( k ), we can substitute these values into the equation ( y = kx ):<\/p>\n\n\n\n [ Solving for ( k ):<\/p>\n\n\n\n [ So, the constant of proportionality is ( k = 7 ).<\/p>\n\n\n\n Now that we know ( k = 7 ), we can use the equation ( y = kx ) to find the value of ( x ) when ( y = 105 ). Substituting the values into the equation:<\/p>\n\n\n\n [ To solve for ( x ), divide both sides of the equation by 7:<\/p>\n\n\n\n [ Thus, when ( y = 105 ), the value of ( x ) is ( \\boxed{15} ).<\/p>\n\n\n\n This problem demonstrates a direct variation between two variables, ( y ) and ( x ). In a direct variation, the ratio between ( y ) and ( x ) remains constant, meaning that as one variable increases, the other does as well, by the same proportional amount. The key step in solving such problems is to first determine the constant of proportionality (( k )) using the known values of ( x ) and ( y ). Once ( k ) is found, it can be used to calculate unknown values of ( x ) for any corresponding value of ( y ), as shown in the solution.<\/p>\n","protected":false},"excerpt":{"rendered":" The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105? The Correct Answer and Explanation is: The given problem states that the value of ( y ) varies directly with ( x ). This means that there is a […]<\/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-165066","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165066","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=165066"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165066\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165066"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165066"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165066"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
y = kx
]<\/p>\n\n\n\nStep 1: Find the constant of proportionality (( k ))<\/h3>\n\n\n\n
21 = k \\times 3
]<\/p>\n\n\n\n
k = \\frac{21}{3} = 7
]<\/p>\n\n\n\nStep 2: Use the constant to find the value of ( x ) when ( y = 105 )<\/h3>\n\n\n\n
105 = 7x
]<\/p>\n\n\n\n
x = \\frac{105}{7} = 15
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n