{"id":18300,"date":"2025-06-12T22:47:12","date_gmt":"2025-06-12T22:47:12","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=18300"},"modified":"2025-06-12T22:47:13","modified_gmt":"2025-06-12T22:47:13","slug":"4-jack-has-14-coins-in-his-pocket-consisting-entirely-of-dimes-and-quarters","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/4-jack-has-14-coins-in-his-pocket-consisting-entirely-of-dimes-and-quarters\/","title":{"rendered":"4 Jack has 14 coins in his pocket, consisting entirely of dimes and quarters"},"content":{"rendered":"\n<p>4 Jack has 14 coins in his pocket, consisting entirely of dimes and quarters. If he has a total of $2.30 in coins, how many quarters are in his pocket?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>To find how many <strong>quarters<\/strong> Jack has, we can solve the problem using a system of equations.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Define the variables<\/h3>\n\n\n\n<p>Let:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>d<\/strong> = number of dimes<\/li>\n\n\n\n<li><strong>q<\/strong> = number of quarters<\/li>\n<\/ul>\n\n\n\n<p>From the problem:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Jack has <strong>14 coins total<\/strong><br>\u2192 Equation 1:\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003<strong>d + q = 14<\/strong><\/li>\n\n\n\n<li>The <strong>total value is $2.30<\/strong>, or <strong>230 cents<\/strong>\n<ul class=\"wp-block-list\">\n<li>Dimes are worth 10 cents<\/li>\n\n\n\n<li>Quarters are worth 25 cents<br>\u2192 Equation 2:\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003<strong>10d + 25q = 230<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve the system<\/h3>\n\n\n\n<p>Use <strong>Equation 1<\/strong> to express <strong>d<\/strong> in terms of <strong>q<\/strong>:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>d = 14 &#8211; q<\/p>\n<\/blockquote>\n\n\n\n<p>Substitute this into <strong>Equation 2<\/strong>:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>10(14 &#8211; q) + 25q = 230<br>140 &#8211; 10q + 25q = 230<br>140 + 15q = 230<br>15q = 90<br>q = 6<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find the number of dimes<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>d = 14 &#8211; q = 14 &#8211; 6 = 8<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer: <strong>Jack has 6 quarters.<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">300-Word Explanation:<\/h3>\n\n\n\n<p>This problem involves solving a system of equations that represent a real-life scenario: counting coins of different denominations to meet a specific total. We are told that Jack has 14 coins in total, and they are only dimes (worth 10 cents) and quarters (worth 25 cents). Altogether, the coins add up to $2.30, which is 230 cents.<\/p>\n\n\n\n<p>To begin solving, we define two variables: <strong>d<\/strong> for the number of dimes, and <strong>q<\/strong> for the number of quarters. From the total number of coins, we know that <strong>d + q = 14<\/strong>. From the total value, we get another equation: the value of the dimes plus the value of the quarters equals 230 cents. This gives us <strong>10d + 25q = 230<\/strong>.<\/p>\n\n\n\n<p>We now have a system of two equations:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>d + q = 14<\/li>\n\n\n\n<li>10d + 25q = 230<\/li>\n<\/ol>\n\n\n\n<p>To solve, we isolate <strong>d<\/strong> from the first equation, giving <strong>d = 14 &#8211; q<\/strong>, and substitute this into the second equation. This replacement eliminates one variable, allowing us to solve for <strong>q<\/strong>. Doing the arithmetic carefully, we find <strong>q = 6<\/strong>, meaning Jack has 6 quarters.<\/p>\n\n\n\n<p>To confirm the solution, we find <strong>d = 14 &#8211; 6 = 8<\/strong> dimes. Then, compute the total value:<br>6 quarters = 6 \u00d7 25 = 150 cents<br>8 dimes = 8 \u00d7 10 = 80 cents<br>Total = 150 + 80 = 230 cents = $2.30<\/p>\n\n\n\n<p>Thus, the solution is correct: <strong>Jack has 6 quarters<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>4 Jack has 14 coins in his pocket, consisting entirely of dimes and quarters. If he has a total of $2.30 in coins, how many quarters are in his pocket? The correct answer and explanation is: To find how many quarters Jack has, we can solve the problem using a system of equations. Step 1: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-18300","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18300","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=18300"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18300\/revisions"}],"predecessor-version":[{"id":18301,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18300\/revisions\/18301"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18300"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18300"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}