{"id":33634,"date":"2020-03-15T16:57:14","date_gmt":"2020-03-15T20:57:14","guid":{"rendered":"https:\/\/www.myedme.com\/login\/?p=33634"},"modified":"2020-03-15T16:57:14","modified_gmt":"2020-03-15T20:57:14","slug":"problems-coins-stamps-and-tickets","status":"publish","type":"post","link":"https:\/\/myedme.com\/login\/problems-coins-stamps-and-tickets\/","title":{"rendered":"Problems: Coins, Stamps and Tickets"},"content":{"rendered":"\n<p>Adalberto\nhas $2.25 in dimes and nickels in his pocket. He has nine\nmore nickels than dimes. How many of each type of coin does he have?<\/p>\n\n\n\n<p><strong>A Complete Solution to Consider<\/strong><\/p>\n\n\n\n<p>Step\n1. <strong>Read<\/strong> the problem. Make sure you understand all the words and ideas.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Determine the types of coins involved.<\/li><\/ul>\n\n\n\n<p>Think\nabout the strategies you have used before. The first thing you need is to\nnotice what types of coins are involved. Adalberto has dimes and nickels.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Create a table<\/strong> to organize the information. <ul><li>Label the columns: We use  &#8220;Type&#8221;, &#8220;Number&#8221;, &#8220;Value&#8221;, &#8220;Total Value&#8221;<\/li><li>List the information you are organizing, in this case coins (Dimes and Nickels).<\/li><li>Write in the information you have about these variables:<ul><li>The value of each type of coin<\/li><li>The total value of all the coins<\/li><\/ul><\/li><\/ul><\/li><\/ul>\n\n\n\n<p>We\ncan work this problem all in cents or in dollars. Here we will do it in dollars\nand put in the dollar sign ($) in the table as a reminder.<\/p>\n\n\n\n<p>The value of a dime is $0.10 and the value of a nickel is $0.05. The total value of all the coins is $2.25.<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter is-style-stripes\"><table class=\"\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Type<\/strong><\/td><td><strong>Number<\/strong><\/td><td><strong>Value<\/strong><\/td><td><strong>Total Value<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Dimes<\/td><td><\/td><td>$0.10<\/td><td><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Nickels<\/td><td><\/td><td>$0.05<\/td><td><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td><\/td><td><\/td><td>$2.25<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Step\n2. <strong>Identify<\/strong> what you are looking for.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>We are asked to find the number of dimes and nickels\n     Adalberto has.<\/li><\/ul>\n\n\n\n<p>Step\n3. <strong>Name<\/strong> what you are looking for.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Use variable expressions to represent the number of  each type of coin.<\/li><li>Multiply the number times the value to get the total value of each type of coin.<\/li><\/ul>\n\n\n\n<p>In this problem you cannot count each type of coin\u2014that is what you are looking for\u2014but you have a clue. There are nine more nickels than dimes. The number of nickels is nine more than the number of dimes.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Let <em>d<\/em> = number of dimes.<\/li><li><em>d<\/em> + 9 = number of nickels<\/li><\/ul>\n\n\n\n<p>Fill in the \u201cnumber\u201d column to help get everything organized.<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter is-style-stripes\"><table class=\"\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Type<\/strong><\/td><td><strong>Number<\/strong><\/td><td><strong>Value<\/strong><\/td><td><strong>Total Value<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Dimes<\/td><td><em>d<\/em><\/td><td>$0.10<\/td><td><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Nickels<\/td><td><em>d<\/em> + 9<\/td><td>$0.05<\/td><td><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td><\/td><td><\/td><td>$2.25<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Now\nwe have all the information we need from the problem! <\/p>\n\n\n\n<p>You\nmultiply the number times the value to get the total value of each type of\ncoin. While you do not know the actual number, you do have an expression to\nrepresent it.<\/p>\n\n\n\n<p>And so now multiply number\u00b7value and write the results in the Total Value column.<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter is-style-stripes\"><table class=\"\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Type<\/strong><\/td><td><strong>Number<\/strong><\/td><td><strong>Value<\/strong><\/td><td><strong>Total Value<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Dimes<\/td><td><em>d<\/em><\/td><td>$0.10<\/td><td>0.10<em>d<\/em><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Nickels<\/td><td><em>d<\/em> + 9<\/td><td>$0.05<\/td><td>0.5(<em>d<\/em> + 9)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td><\/td><td><\/td><td>$2.25<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Step\n4. <strong>Translate<\/strong> into an equation. Restate the problem in one sentence. Then\ntranslate into an equation.<\/p>\n\n\n\n<p class=\"has-text-align-center\">0.10d + 0.05(d + 9) = 2.25<\/p>\n\n\n\n<p>Step 5. <strong>Solve<\/strong> the equation using good algebra techniques.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Write the equation.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a00.10<em>d<\/em> + 0.05(<em>d<\/em> + 9) = 2.25<\/li><li>Distribute.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a00.10<em>d<\/em> + 0.05<em>d<\/em> + 0.45 = 2.25<\/li><li>Combine like terms.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0.15<em>d<\/em> + 0.45 = 2.25<\/li><li>Subtract 0.45 from each side.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0  0.15<em>d<\/em> = 1.80<\/li><li>Divide to find the number of dimes.\u00a0 <em>d<\/em> = 12<\/li><li>The number of nickels is <em>d<\/em> + 9\u00a0.        So, 12 + 9 = 21 nickels.<\/li><\/ul>\n\n\n\n<p>Step\n6. <strong>Check.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>12 dimes: 12(0.10) = 1.20<\/li><li>21 nickels: 21(0.05) = 1.05\u00a0 and $1.20 + $1.05 = $2.25\u2713<\/li><\/ul>\n\n\n\n<p>Step\n7. <strong>Answer<\/strong> the question.<\/p>\n\n\n\n<p><em>Adalberto has twelve dimes and twenty-one nickels.<\/em><\/p>\n\n\n\n<p><strong>Now it&#8217;s Your Turn!! <\/strong>Liliana has $2.10 in nickels and quarters in her backpack. She has 12 more nickels than quarters. How many coins of each type does she have?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Adalberto has $2.25 in dimes and nickels in his pocket. He has nine more nickels than dimes. How many of each type of coin does he have? A Complete Solution to Consider Step 1. Read the problem. Make sure you understand all the words and ideas. Determine the types of coins involved. Think about the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-33634","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33634","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/comments?post=33634"}],"version-history":[{"count":1,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33634\/revisions"}],"predecessor-version":[{"id":33639,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/posts\/33634\/revisions\/33639"}],"wp:attachment":[{"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/media?parent=33634"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/categories?post=33634"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/myedme.com\/login\/wp-json\/wp\/v2\/tags?post=33634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}