At the present time, Mrs. Bee’s age is six years more than four times her son’s age. Three years
ago, she was seven times as old as her son was then. If (b) represents Mrs. Bee’s age now and (s)
represents her son’s age now, write a system of equations that could be used to model this
scenario. Use this system of equations to determine, algebraically, the ages of both Mrs. Bee
and her son now. Determine how many years from now Mrs. Bee will be three times as old as
her son will be then.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: 38 years old<\/strong>, and her son is 8 years old<\/strong>. In 7 years<\/strong><\/p>\n\n\n\n To model the scenario involving Mrs. Bee and her son, we can set up a system of equations based on the information provided. Let ( b ) represent Mrs. Bee’s current age and ( s ) represent her son’s current age.<\/p>\n\n\n\n Now we have the system of equations:<\/p>\n\n\n\n [ First, let’s simplify equation (2):<\/p>\n\n\n\n [ Now we have two expressions for ( b ):<\/p>\n\n\n\n Setting them equal to each other:<\/p>\n\n\n\n [ Rearranging this gives:<\/p>\n\n\n\n [ Now that we have ( s ), we can find ( b ):<\/p>\n\n\n\n [ Thus, Mrs. Bee’s current age is ( 38 ) years, and her son is ( 8 ) years old.<\/p>\n\n\n\n To determine how many years from now Mrs. Bee will be three times as old as her son, we need to set up the following equation:<\/p>\n\n\n\n Let ( x ) be the number of years from now. Then:<\/p>\n\n\n\n [ Substituting the known values of ( b ) and ( s ):<\/p>\n\n\n\n [ Rearranging gives:<\/p>\n\n\n\n [ Therefore, in 7 years<\/strong>, Mrs. Bee will be three times as old as her son.<\/p>\n\n\n\n In summary, Mrs. Bee is currently 38 years old<\/strong>, and her son is 8 years old<\/strong>. In 7 years<\/strong>, Mrs. Bee will be three times the age of her son.<\/p>\n","protected":false},"excerpt":{"rendered":" At the present time, Mrs. Bee’s age is six years more than four times her son’s age. Three yearsago, she was seven times as old as her son was then. If (b) represents Mrs. Bee’s age now and (s)represents her son’s age now, write a system of equations that could be used to model thisscenario. […]<\/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-152257","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152257","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=152257"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152257\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152257"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152257"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152257"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Setting Up the Equations<\/h3>\n\n\n\n
\n
[
b = 4s + 6
]<\/li>\n\n\n\n
[
b – 3 = 7(s – 3)
]<\/li>\n<\/ol>\n\n\n\n
\\begin{align} (1) & \\quad b = 4s + 6 \\ (2) & \\quad b – 3 = 7(s – 3) \\end{align<\/em>}
]<\/p>\n\n\n\nSolving the System of Equations<\/h3>\n\n\n\n
b – 3 = 7(s – 3) \\implies b – 3 = 7s – 21 \\implies b = 7s – 18
]<\/p>\n\n\n\n\n
4s + 6 = 7s – 18
]<\/p>\n\n\n\n
6 + 18 = 7s – 4s \\implies 24 = 3s \\implies s = 8
]<\/p>\n\n\n\n
b = 4s + 6 = 4(8) + 6 = 32 + 6 = 38
]<\/p>\n\n\n\nFuture Age Calculation<\/h3>\n\n\n\n
b + x = 3(s + x)
]<\/p>\n\n\n\n
38 + x = 3(8 + x) \\implies 38 + x = 24 + 3x
]<\/p>\n\n\n\n
38 – 24 = 3x – x \\implies 14 = 2x \\implies x = 7
]<\/p>\n\n\n\nSummary<\/h3>\n\n\n\n