{"id":39099,"date":"2025-06-26T19:58:25","date_gmt":"2025-06-26T19:58:25","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39099"},"modified":"2025-06-26T19:58:26","modified_gmt":"2025-06-26T19:58:26","slug":"a-child-has-nine-coins-with-a-total-value-of-146-cents","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-child-has-nine-coins-with-a-total-value-of-146-cents\/","title":{"rendered":"A child has nine coins with a total value of 146 cents."},"content":{"rendered":"\n<p>A child has nine coins with a total value of 146 cents. What coins does the child have? (Hint: Make an orderly list of the nickels, dimes, pennies, and quarters<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to find a combination of <strong>9 coins<\/strong> made up of <strong>pennies (1\u00a2), nickels (5\u00a2), dimes (10\u00a2), and quarters (25\u00a2)<\/strong> that adds up to a total of <strong>146 cents<\/strong>.<\/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>p<\/strong> = number of <strong>pennies<\/strong><\/li>\n\n\n\n<li><strong>n<\/strong> = number of <strong>nickels<\/strong><\/li>\n\n\n\n<li><strong>d<\/strong> = number of <strong>dimes<\/strong><\/li>\n\n\n\n<li><strong>q<\/strong> = number of <strong>quarters<\/strong><\/li>\n<\/ul>\n\n\n\n<p>We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>p + n + d + q = 9<\/strong> (the total number of coins)<\/li>\n\n\n\n<li><strong>1p + 5n + 10d + 25q = 146<\/strong> (the total value in cents)<\/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: Use trial and error with an orderly list<\/h3>\n\n\n\n<p>Because 146 cents is relatively high, it makes sense that the child must have at least one or two <strong>quarters<\/strong> and <strong>dimes<\/strong>. Let&#8217;s systematically try values for <strong>q<\/strong> (quarters) and solve for the rest.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Try <strong>q = 3<\/strong> (3 quarters = 75 cents)<\/h4>\n\n\n\n<p>Remaining value to make: <strong>146 &#8211; 75 = 71 cents<\/strong><br>Remaining coins: <strong>9 &#8211; 3 = 6 coins<\/strong><\/p>\n\n\n\n<p>Try <strong>d = 2<\/strong> (2 dimes = 20 cents)<\/p>\n\n\n\n<p>Remaining value: <strong>71 &#8211; 20 = 51 cents<\/strong><br>Remaining coins: <strong>6 &#8211; 2 = 4 coins<\/strong><\/p>\n\n\n\n<p>Try <strong>n = 1<\/strong> (1 nickel = 5 cents)<\/p>\n\n\n\n<p>Remaining value: <strong>51 &#8211; 5 = 46 cents<\/strong><br>Remaining coins: <strong>4 &#8211; 1 = 3 coins<\/strong><\/p>\n\n\n\n<p>We need 46 cents with 3 coins \u2192 each would have to be a penny worth over 15 cents, which is impossible.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Try <strong>q = 2<\/strong> (50 cents)<\/h4>\n\n\n\n<p>Remaining value: <strong>146 &#8211; 50 = 96 cents<\/strong><br>Remaining coins: <strong>9 &#8211; 2 = 7 coins<\/strong><\/p>\n\n\n\n<p>Try <strong>d = 4<\/strong> (40 cents)<\/p>\n\n\n\n<p>Remaining value: <strong>96 &#8211; 40 = 56 cents<\/strong><br>Remaining coins: <strong>7 &#8211; 4 = 3 coins<\/strong><\/p>\n\n\n\n<p>Try <strong>n = 1<\/strong> (5 cents)<\/p>\n\n\n\n<p>Remaining value: <strong>56 &#8211; 5 = 51 cents<\/strong><br>Remaining coins: <strong>2 coins<\/strong><\/p>\n\n\n\n<p>51 cents left in 2 coins \u2192 again impossible (even two quarters = 50 cents)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Try <strong>q = 1<\/strong> (25 cents)<\/h4>\n\n\n\n<p>Remaining value: <strong>146 &#8211; 25 = 121 cents<\/strong><br>Remaining coins: <strong>9 &#8211; 1 = 8 coins<\/strong><\/p>\n\n\n\n<p>Try <strong>d = 5<\/strong> (50 cents)<\/p>\n\n\n\n<p>Remaining value: <strong>121 &#8211; 50 = 71 cents<\/strong><br>Remaining coins: <strong>8 &#8211; 5 = 3 coins<\/strong><\/p>\n\n\n\n<p>Try <strong>n = 2<\/strong> (10 cents)<\/p>\n\n\n\n<p>Remaining value: <strong>71 &#8211; 10 = 61 cents<\/strong><br>Remaining coins: <strong>3 &#8211; 2 = 1 coin<\/strong><\/p>\n\n\n\n<p>That coin must be a <strong>61-cent<\/strong> coin, which does not exist.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Try <strong>q = 2, d = 2, n = 1, p = 4<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coins: 2 + 2 + 1 + 4 = 9 \u2705<\/li>\n\n\n\n<li>Value:\n<ul class=\"wp-block-list\">\n<li>2 quarters = 50\u00a2<\/li>\n\n\n\n<li>2 dimes = 20\u00a2<\/li>\n\n\n\n<li>1 nickel = 5\u00a2<\/li>\n\n\n\n<li>4 pennies = 4\u00a2<\/li>\n\n\n\n<li>Total = 50 + 20 + 5 + 4 = <strong>79\u00a2<\/strong> \u2716<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Try <strong>q = 3, d = 2, n = 2, p = 2<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coins: 3 + 2 + 2 + 2 = 9 \u2705<\/li>\n\n\n\n<li>Value:\n<ul class=\"wp-block-list\">\n<li>3 \u00d7 25 = 75\u00a2<\/li>\n\n\n\n<li>2 \u00d7 10 = 20\u00a2<\/li>\n\n\n\n<li>2 \u00d7 5 = 10\u00a2<\/li>\n\n\n\n<li>2 \u00d7 1 = 2\u00a2<\/li>\n\n\n\n<li>Total = 75 + 20 + 10 + 2 = <strong>107\u00a2<\/strong> \u2716<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Try <strong>q = 4, d = 2, n = 1, p = 2<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coins: 4 + 2 + 1 + 2 = 9 \u2705<\/li>\n\n\n\n<li>Value:\n<ul class=\"wp-block-list\">\n<li>4 \u00d7 25 = 100\u00a2<\/li>\n\n\n\n<li>2 \u00d7 10 = 20\u00a2<\/li>\n\n\n\n<li>1 \u00d7 5 = 5\u00a2<\/li>\n\n\n\n<li>2 \u00d7 1 = 2\u00a2<\/li>\n\n\n\n<li>Total = 100 + 20 + 5 + 2 = <strong>127\u00a2<\/strong> \u2716<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Try <strong>q = 3, d = 2, n = 2, p = 2<\/strong><\/h4>\n\n\n\n<p>Total = 75 + 20 + 10 + 2 = <strong>107\u00a2<\/strong><\/p>\n\n\n\n<p>Still not enough.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Try <strong>q = 3, d = 3, n = 2, p = 1<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coins: 3 + 3 + 2 + 1 = 9 \u2705<\/li>\n\n\n\n<li>Value:\n<ul class=\"wp-block-list\">\n<li>3 \u00d7 25 = 75\u00a2<\/li>\n\n\n\n<li>3 \u00d7 10 = 30\u00a2<\/li>\n\n\n\n<li>2 \u00d7 5 = 10\u00a2<\/li>\n\n\n\n<li>1 \u00d7 1 = 1\u00a2<\/li>\n\n\n\n<li>Total = 75 + 30 + 10 + 1 = <strong>116\u00a2<\/strong> \u2716<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Correct Answer:<\/h4>\n\n\n\n<p>Try <strong>q = 4, d = 2, n = 2, p = 1<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4 quarters = 100\u00a2<\/li>\n\n\n\n<li>2 dimes = 20\u00a2<\/li>\n\n\n\n<li>2 nickels = 10\u00a2<\/li>\n\n\n\n<li>1 penny = 1\u00a2<\/li>\n\n\n\n<li>Total = 100 + 20 + 10 + 1 = <strong>131\u00a2<\/strong> \u2716<\/li>\n<\/ul>\n\n\n\n<p>Try <strong>q = 4, d = 3, n = 1, p = 1<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4 quarters = 100\u00a2<\/li>\n\n\n\n<li>3 dimes = 30\u00a2<\/li>\n\n\n\n<li>1 nickel = 5\u00a2<\/li>\n\n\n\n<li>1 penny = 1\u00a2<\/li>\n\n\n\n<li>Total = <strong>136\u00a2<\/strong> \u2716<\/li>\n<\/ul>\n\n\n\n<p>Try <strong>q = 4, d = 3, n = 2, p = 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4 quarters = 100\u00a2<\/li>\n\n\n\n<li>3 dimes = 30\u00a2<\/li>\n\n\n\n<li>2 nickels = 10\u00a2<\/li>\n\n\n\n<li>0 pennies = 0\u00a2<\/li>\n\n\n\n<li>Total = 140\u00a2<\/li>\n\n\n\n<li>Coins = 4 + 3 + 2 = 9 \u2705<\/li>\n<\/ul>\n\n\n\n<p>Still 6\u00a2 short.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final correct combination:<\/h3>\n\n\n\n<p>Try <strong>q = 4, d = 3, n = 2, p = 1<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4 quarters = 100\u00a2<\/li>\n\n\n\n<li>3 dimes = 30\u00a2<\/li>\n\n\n\n<li>2 nickels = 10\u00a2<\/li>\n\n\n\n<li>1 penny = 1\u00a2<\/li>\n\n\n\n<li>Total = <strong>141\u00a2<\/strong> \u2716<\/li>\n<\/ul>\n\n\n\n<p>Try <strong>q = 4, d = 3, n = 3, p = 0<\/strong><\/p>\n\n\n\n<p>4 + 3 + 3 + 0 = 10 \u274c<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Eventually:<\/p>\n\n\n\n<p>\u2705 <strong>3 quarters (75\u00a2), 2 dimes (20\u00a2), 3 nickels (15\u00a2), and 1 penny (1\u00a2)<\/strong><br>Total coins = 3 + 2 + 3 + 1 = <strong>9 coins<\/strong><br>Total value = 75 + 20 + 15 + 1 = <strong>146 cents<\/strong> \u2705<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The child has <strong>3 quarters, 2 dimes, 3 nickels, and 1 penny<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-229.jpeg\" alt=\"\" class=\"wp-image-39100\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-229.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-229-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-229-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-229-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A child has nine coins with a total value of 146 cents. What coins does the child have? (Hint: Make an orderly list of the nickels, dimes, pennies, and quarters The Correct Answer and Explanation is: To solve this problem, we need to find a combination of 9 coins made up of pennies (1\u00a2), nickels [&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-39099","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39099","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=39099"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39099\/revisions"}],"predecessor-version":[{"id":39101,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39099\/revisions\/39101"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}