{"id":271728,"date":"2025-07-26T06:29:08","date_gmt":"2025-07-26T06:29:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271728"},"modified":"2025-07-26T06:29:10","modified_gmt":"2025-07-26T06:29:10","slug":"at-a-certain-store-4-knives-5-spoons-and-6-forks-cost-7-90","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/26\/at-a-certain-store-4-knives-5-spoons-and-6-forks-cost-7-90\/","title":{"rendered":"At a certain store, 4 knives, 5 spoons, and 6 forks cost $7.90"},"content":{"rendered":"\n<p>At a certain store, 4 knives, 5 spoons, and 6 forks cost $7.90. To purchase 2 knives, 2 spoons, and 5 forks would cost $5.80. How much do 2 knives, 3 spoons, and 1 fork cost?<br>A $2.10<br>B $3.30<br>C $4.70<br>D $5.80<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we can use a system of linear equations. Let&#8217;s define the cost of each item:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let the cost of one knife be kk,<\/li>\n\n\n\n<li>Let the cost of one spoon be ss,<\/li>\n\n\n\n<li>Let the cost of one fork be ff.<\/li>\n<\/ul>\n\n\n\n<p>We are given two conditions in the problem:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The total cost of 4 knives, 5 spoons, and 6 forks is $7.90: 4k+5s+6f=7.904k + 5s + 6f = 7.90<\/li>\n\n\n\n<li>The total cost of 2 knives, 2 spoons, and 5 forks is $5.80: 2k+2s+5f=5.802k + 2s + 5f = 5.80<\/li>\n<\/ol>\n\n\n\n<p>We need to find the cost of 2 knives, 3 spoons, and 1 fork: 2k+3s+f2k + 3s + f<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Eliminate one variable<\/h3>\n\n\n\n<p>Start by simplifying and solving the equations. First, let&#8217;s multiply the second equation by 2 to make the number of knives equal in both equations: 2(2k+2s+5f)=2(5.80)2(2k + 2s + 5f) = 2(5.80) 4k+4s+10f=11.604k + 4s + 10f = 11.60<\/p>\n\n\n\n<p>Now subtract the first equation from this new equation to eliminate kk: (4k+4s+10f)\u2212(4k+5s+6f)=11.60\u22127.90(4k + 4s + 10f) &#8211; (4k + 5s + 6f) = 11.60 &#8211; 7.90 (4k\u22124k)+(4s\u22125s)+(10f\u22126f)=3.70(4k &#8211; 4k) + (4s &#8211; 5s) + (10f &#8211; 6f) = 3.70 \u2212s+4f=3.70-s + 4f = 3.70<\/p>\n\n\n\n<p>This simplifies to: s=4f\u22123.70s = 4f &#8211; 3.70<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Substitute into one of the original equations<\/h3>\n\n\n\n<p>Substitute s=4f\u22123.70s = 4f &#8211; 3.70 into the first equation 4k+5s+6f=7.904k + 5s + 6f = 7.90: 4k+5(4f\u22123.70)+6f=7.904k + 5(4f &#8211; 3.70) + 6f = 7.90 4k+20f\u221218.50+6f=7.904k + 20f &#8211; 18.50 + 6f = 7.90 4k+26f\u221218.50=7.904k + 26f &#8211; 18.50 = 7.90 4k+26f=26.404k + 26f = 26.40<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solve for kk<\/h3>\n\n\n\n<p>Now divide both sides by 4: k+6.5f=6.60k + 6.5f = 6.60 k=6.60\u22126.5fk = 6.60 &#8211; 6.5f<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Solve for the cost of 2 knives, 3 spoons, and 1 fork<\/h3>\n\n\n\n<p>Now substitute k=6.60\u22126.5fk = 6.60 &#8211; 6.5f and s=4f\u22123.70s = 4f &#8211; 3.70 into the expression for the cost of 2 knives, 3 spoons, and 1 fork: 2k+3s+f=2(6.60\u22126.5f)+3(4f\u22123.70)+f2k + 3s + f = 2(6.60 &#8211; 6.5f) + 3(4f &#8211; 3.70) + f =13.20\u221213f+12f\u221211.10+f= 13.20 &#8211; 13f + 12f &#8211; 11.10 + f =13.20\u221211.10=2.10= 13.20 &#8211; 11.10 = 2.10<\/p>\n\n\n\n<p>Thus, the cost of 2 knives, 3 spoons, and 1 fork is <strong>$2.10<\/strong>.<\/p>\n\n\n\n<p>The correct answer is <strong>A<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>At a certain store, 4 knives, 5 spoons, and 6 forks cost $7.90. To purchase 2 knives, 2 spoons, and 5 forks would cost $5.80. How much do 2 knives, 3 spoons, and 1 fork cost?A $2.10B $3.30C $4.70D $5.80 The correct answer and explanation is: To solve this problem, we can use a system [&hellip;]<\/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-271728","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271728","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=271728"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271728\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271728"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271728"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271728"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}