{"id":11039,"date":"2022-06-15T19:26:19","date_gmt":"2022-06-15T13:56:19","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11039"},"modified":"2022-06-15T19:26:23","modified_gmt":"2022-06-15T13:56:23","slug":"form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/","title":{"rendered":"Form the pair of linear equations for the following problems and find their solution by substitution method."},"content":{"rendered":"

Question<\/strong> :\u00a0 Form the pair of linear equations for the following problems and find their solution by substitution method.<\/p>\n

(i)<\/strong>\u00a0 The difference between two numbers is 26 and one number is three times the other. Find them.<\/p>\n

(ii)<\/strong>\u00a0 The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.<\/p>\n

(iii)<\/strong>\u00a0 The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.<\/p>\n

(iv)<\/strong>\u00a0 The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charges per kilometer ? How much does a person have to pay for travelling a distance of 25 km ?<\/p>\n

(v)<\/strong>\u00a0 A fraction becomes \\(9\\over 11\\), if 2 is added to both the numerator and denominator. If 3 is added to both the numerator and denominator it becomes \\(5\\over 6\\). Find the fraction.<\/p>\n

(vi)<\/strong>\u00a0 Five years hence, the age of Jacob will be three times that of son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages.<\/p>\n

Solution :<\/h2>\n

(i)<\/strong>\u00a0 Let x and y be the numbers.<\/p>\n

And the difference of two numbers is 26.<\/p>\n

i.e.\u00a0 x – y = 26\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ………(1)<\/p>\n

One number is three times the other.<\/p>\n

i.e.\u00a0 x = 3y\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0………(2)<\/p>\n

Putting x = 3y in equation (1)\u00a0 we get<\/p>\n

3y – y = 26\u00a0 \\(\\implies\\)\u00a0 2y = 26\u00a0 \\(\\implies\\)\u00a0 y =13<\/p>\n

Now, put the value of y = 13 in equation (2), we get\u00a0 x = 39<\/p>\n

Hence, the numbers are x = 39 and y = 13<\/strong>.<\/p>\n

(ii)<\/strong>\u00a0 Let x and y be the angles. Then,<\/p>\n

ATQ,<\/p>\n

x + y = 180\u00a0 \u00a0 \u00a0 …….(1)<\/p>\n

and\u00a0 x = y + 18\u00a0 \u00a0 \u00a0 \u00a0 ……(2)<\/p>\n

Putting x = y + 18 in equation (1)\u00a0 we get<\/p>\n

y + 18 + y = 180<\/p>\n

2y = 180 – 18\u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a02y = 162\u00a0 \u00a0\\(\\implies\\)\u00a0 y = 81<\/p>\n

Now, put the value of y = 81 in equation (2), we get<\/p>\n

x = 81 + 18 = 90<\/p>\n

Hence, the angles are x = 99 degrees and y = 81 degrees<\/strong>.<\/p>\n

(iii)<\/strong>\u00a0 Let x be the cost of one bat and y be the cost of one ball respectively. Then,<\/p>\n

7x + 6y = 3800\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ………(1)<\/p>\n

i.e.\u00a0 3x + 5y = 1750\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0………(2)<\/p>\n

From equation (2), y = \\(1750 – 3x\\over 5\\)<\/p>\n

Substituting the value of y = \\(1750 – 3x\\over 5\\) in equation (1), we get<\/p>\n

35x + 10500 – 18x = 19000<\/p>\n

\\(\\implies\\)\u00a0 17x = 8500\u00a0 \\(\\implies\\)\u00a0 x = 500<\/p>\n

Now, put the value of x = 500 in equation (2), we get<\/p>\n

3(500) + 5y = 1750\u00a0 \\(\\implies\\)\u00a0 5y = 250\u00a0 \\(\\implies\\)\u00a0 y = 50<\/p>\n

Hence, the cost of one bat is 500 Rupees and the cost of one ball is 50 Rupees<\/strong>.<\/p>\n

(iv)<\/strong>\u00a0 Let x Rs be the fixed charges of taxi and<\/p>\n

the y Rs be the running charges of taxi per km.<\/p>\n

ATQ,<\/p>\n

Expenses of travelling 10 km = 105 Rs<\/p>\n

i.e.\u00a0 \u00a0x + 10y = 105\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ……(i)<\/p>\n

Again the expenses of travelling 15 km = 155 Rs<\/p>\n

i.e.\u00a0 \u00a0x + 15y = 155\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ……..(ii)<\/p>\n

Putting the value of x = 155 – 15y from equation (2) in equation (1), we get<\/p>\n

155 – 15y + 10y = 105<\/p>\n

155 – 5y = 105<\/p>\n

\\(\\implies\\)\u00a0 5y = 50\u00a0 \\(\\implies\\)\u00a0 y = 10<\/p>\n

Now, put the value of y = 10 in equation (2), we get<\/p>\n

x + 15(10) = 155<\/p>\n

\\(\\implies\\) x = 155 – 150 = 5<\/p>\n

Hence, the fixed charges of taxi is 5 Rupees<\/strong> and the running charges of taxi per km is 10 Rupees.<\/strong><\/p>\n

A person have to pay for travelling 25 km = 5 + 25(10) = 5 + 250 = 255 Rupees.<\/strong><\/p>\n

(v)<\/strong>\u00a0 Let x be the numerator and y be the denominator. Then, according to the question,<\/p>\n

CASE 1<\/strong> :\u00a0 \\(x+ 2\\over y + 2\\) = \\(9\\over 11\\)<\/p>\n

\\(\\implies\\)\u00a0 11(x + 2) = 9(y + 2)\u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a011x + 22 = 9y + 18<\/p>\n

\\(\\implies\\)\u00a0 11x – 9y = -4\u00a0 \u00a0 ……(1)<\/p>\n

CASE 2<\/strong> :\u00a0 \\(x + 3\\over y + 3\\) = \\(5\\over 6\\)<\/p>\n

\\(\\implies\\)\u00a0 6(x + 3) = 5(y + 3)\u00a0 \\(\\implies\\)\u00a0 6x + 18 = 5y + 15<\/p>\n

\\(\\implies\\)\u00a0 6x – 5y = – 3<\/p>\n

\\(\\implies\\)\u00a0 x = \\(5y – 3\\over 6\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0……(2)<\/p>\n

Put the value of x = \\(5y – 3\\over 6\\)\u00a0 in equation (1), we get<\/p>\n

11(\\(5y – 3\\over 6\\) ) – 9y = -4<\/p>\n

\\(\\implies\\)\u00a0 11(5y – 3) – 54y = -24<\/p>\n

\\(\\implies\\)\u00a0 55y – 33 – 54 = -24<\/p>\n

\\(\\implies\\)\u00a0 \u00a0y = 33 – 24 = 9<\/p>\n

Putting the value of\u00a0 y = 9 in (1), we get<\/p>\n

11x – 9(9)\u00a0 = – 4<\/p>\n

11x = -4 + 81 = 77<\/p>\n

x = 7<\/p>\n

Hence, \\(7\\over 8\\)<\/strong> is the required fraction.<\/p>\n

(vi)<\/strong>\u00a0 Let Jacob’s present age be x and his son be y.<\/p>\n

CASE 1<\/strong> : After five years age of Jacob = (x + 5),<\/p>\n

After five years the age of his son = (y + 5).<\/p>\n

According question,<\/p>\n

x + 5 = 3(y + 5)<\/p>\n

\\(\\implies\\)\u00a0 x – 3y = 10<\/p>\n

CASE 2<\/strong> : Five years ago Jacob’s age = x – 5, his son’s age = y – 5. Then,<\/p>\n

ATQ,<\/p>\n

x – 5 = 7(y – 5)\u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0x = 7y – 30<\/p>\n

Putting x = 7y – 30\u00a0 from equation (2) in (1), we get<\/p>\n

7y – 30 – 3y = 10<\/p>\n

\\(\\implies\\)\u00a0 4y = 40\u00a0 \u00a0\\(\\implies\\)\u00a0 y = 10<\/p>\n

Now, put y = 10 in equation (1), we get<\/p>\n

x – 3(10) = 10<\/p>\n

\\(\\implies\\)\u00a0 x = 10 + 30 = 40<\/p>\n

Hence, the age of Jacob is 40 years<\/strong>, and age of his son is 10 years.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Question :\u00a0 Form the pair of linear equations for the following problems and find their solution by substitution method. (i)\u00a0 The difference between two numbers is 26 and one number is three times the other. Find them. (ii)\u00a0 The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. (iii)\u00a0 The coach …<\/p>\n

Form the pair of linear equations for the following problems and find their solution by substitution method.<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[911,43],"tags":[],"yoast_head":"\nForm the pair of linear equations for the following problems and find their solution by substitution method. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Form the pair of linear equations for the following problems and find their solution by substitution method. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Question :\u00a0 Form the pair of linear equations for the following problems and find their solution by substitution method. (i)\u00a0 The difference between two numbers is 26 and one number is three times the other. Find them. (ii)\u00a0 The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. (iii)\u00a0 The coach … Form the pair of linear equations for the following problems and find their solution by substitution method. Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-06-15T13:56:19+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-06-15T13:56:23+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Form the pair of linear equations for the following problems and find their solution by substitution method.\",\"datePublished\":\"2022-06-15T13:56:19+00:00\",\"dateModified\":\"2022-06-15T13:56:23+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/\"},\"wordCount\":732,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Linear Equation in Two Variables Questions\",\"Maths Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/\",\"url\":\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/\",\"name\":\"Form the pair of linear equations for the following problems and find their solution by substitution method. - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2022-06-15T13:56:19+00:00\",\"dateModified\":\"2022-06-15T13:56:23+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Form the pair of linear equations for the following problems and find their solution by substitution method.\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Form the pair of linear equations for the following problems and find their solution by substitution method. - Mathemerize","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/","og_locale":"en_US","og_type":"article","og_title":"Form the pair of linear equations for the following problems and find their solution by substitution method. - Mathemerize","og_description":"Question :\u00a0 Form the pair of linear equations for the following problems and find their solution by substitution method. (i)\u00a0 The difference between two numbers is 26 and one number is three times the other. Find them. (ii)\u00a0 The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. (iii)\u00a0 The coach … Form the pair of linear equations for the following problems and find their solution by substitution method. Read More »","og_url":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/","og_site_name":"Mathemerize","article_published_time":"2022-06-15T13:56:19+00:00","article_modified_time":"2022-06-15T13:56:23+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Form the pair of linear equations for the following problems and find their solution by substitution method.","datePublished":"2022-06-15T13:56:19+00:00","dateModified":"2022-06-15T13:56:23+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/"},"wordCount":732,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Linear Equation in Two Variables Questions","Maths Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/","url":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/","name":"Form the pair of linear equations for the following problems and find their solution by substitution method. - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2022-06-15T13:56:19+00:00","dateModified":"2022-06-15T13:56:23+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/form-the-pair-of-linear-equations-for-the-following-problems-and-find-their-solution-by-substitution-method\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Form the pair of linear equations for the following problems and find their solution by substitution method."}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/11039"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=11039"}],"version-history":[{"count":3,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/11039\/revisions"}],"predecessor-version":[{"id":11051,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/11039\/revisions\/11051"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=11039"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=11039"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=11039"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}