{"id":4638,"date":"2020-04-21T00:19:13","date_gmt":"2020-04-21T00:19:13","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/putting-it-together-general-problem-solving\/"},"modified":"2020-04-21T00:19:13","modified_gmt":"2020-04-21T00:19:13","slug":"putting-it-together-general-problem-solving","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/putting-it-together-general-problem-solving\/","title":{"raw":"Taxes","rendered":"Taxes"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate sales and income taxes&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7041,&quot;3&quot;:{&quot;1&quot;:0},&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Calculate sales and income taxes<\/span><\/li>\n<\/ul>\n<\/div>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/27192407\/5120304358_f64b93a2ec_o.jpg\"><img class=\" wp-image-2212 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/27192407\/5120304358_f64b93a2ec_o-300x212.jpg\" alt=\"magnifying lens over the word &quot;tax&quot;\" width=\"442\" height=\"312\"><\/a>\n\nGovernments collect taxes to pay for the services they provide. In the United States, federal income taxes help fund the military, the environmental protection agency, and thousands of other programs. Property taxes help fund schools. Gasoline taxes help pay for road improvements. While very few people enjoy paying taxes, they are necessary to pay for the services we all depend upon.\n\nTaxes can be computed in a variety of ways, but are typically computed as a percentage of a sale, of one\u2019s income, or of one\u2019s assets.\n<div class=\"textbox examples\">\n<h3>recall calculations with percents<\/h3>\nTo make calculations using percents, first convert the percent to a decimal by dropping the % symbol and moving the decimal two places to the left (adding more zeros to the left as needed).\n\nEx. Write 2.7% as a decimal\n\nWrite 02.7 then move the decimal two places left to divide by 100.\n\n0.027 is the decimal representation of 2.7%.\n\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Sales Tax<\/h3>\nThe sales tax rate in a city is 9.3%. How much sales tax will you pay on a $140 purchase?\n[reveal-answer q=\"620729\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"620729\"]\n\nThe sales tax will be 9.3% of $140. To compute this, we multiply $140 by the percent written as a decimal: $140(0.093) = $13.02.\n\n[\/hidden-answer][ohm_question]80109[\/ohm_question]\n\n<\/div>\nWhen taxes are not given as a fixed percentage rate, sometimes it is necessary to calculate the <strong>effective tax rate<\/strong>:<strong>&nbsp;<\/strong>the equivalent percent rate of the tax paid out of the dollar amount the tax is based on.\n<div class=\"textbox examples\">\n<h3>Write a ratio as a percent<\/h3>\nTo obtain a percent from a ratio, divide the part by the whole and multiply by 100.\n\nEx. If 87 out of 932 people polled claim to dislike pizza, the percent of people polled who stated they don't like pizza is:\n\n[latex]\\dfrac{\\text{ part }}{\\text{ whole }}=\\dfrac{87}{932} \\approx .0934[\/latex]\n\n[latex].0934 \\cdot 100 = 9.34 \\%[\/latex].\n\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Property Tax<\/h3>\nJaquim&nbsp;paid $3,200 in property taxes on his&nbsp;house valued at $215,000 last year. What is the effective tax rate?\n[reveal-answer q=\"696377\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"696377\"]\n\nWe can compute the equivalent percentage: 3200\/215000 = 0.01488, or about 1.49% effective rate.\n\n[\/hidden-answer]\n\n<\/div>\nTaxes are often referred to as progressive, regressive, or flat.\n<ul>\n \t<li>A <strong>flat tax<\/strong>, or proportional tax, charges a constant percentage rate.<\/li>\n \t<li>A <strong>progressive tax<\/strong> increases the percent rate as the base amount increases.<\/li>\n \t<li>A <strong>regressive tax <\/strong>decreases the percent rate as the base amount increases.<\/li>\n<\/ul>\n<div class=\"textbox exercises\">\n<h3>Example: Federal Income Tax<\/h3>\nThe United States federal income tax on earned wages is an example of a progressive tax. People with a higher wage income pay a higher percent tax on their income.\n\nFor a single person in 2011, adjusted gross income (income after deductions) under $8,500 was taxed at 10%. Income over $8,500 but under $34,500 was taxed at 15%.\n<h4>Earning $10,000<\/h4>\nStephen earned&nbsp;$10,000 in 2011. He would pay 10% on the portion of his&nbsp;income under $8,500, and 15% on the income over $8,500.\n\n8500(0.10) = 850 &nbsp; &nbsp; 10% of $8500\n1500(0.15) = 225 &nbsp; &nbsp; &nbsp;15% of the remaining $1500 of income\nTotal tax:&nbsp;&nbsp; = $1075\n\nWhat was Stephen's effective tax rate?\n[reveal-answer q=\"696772\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"696772\"]<p>The effective tax rate paid is 1075\/10000 = 10.75%<\/p>[\/hidden-answer]\n\n&nbsp;\n<h4>Earning $30,000<\/h4>\nD'Andrea&nbsp;earned $30,000 in 2011. She would also pay 10% on the portion of her&nbsp;income under $8,500, and 15% on the income over $8,500.\n\n8500(0.10) = 850&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 10% of $8500\n21500(0.15) = 3225&nbsp;&nbsp;&nbsp; 15% of the remaining $21500 of income\nTotal tax:&nbsp;&nbsp; = $4075\n\nWhat was D'Andrea's effective tax rate?\n[reveal-answer q=\"648795\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"648795\"]<p>The effective tax rate paid is 4075\/30000 = 13.58%.<\/p>[\/hidden-answer]\n\n&nbsp;\n\nNotice that the effective rate has increased with income, showing this is a progressive tax.\n\n<\/div>\n&nbsp;\n<div class=\"textbox exercises\">\n<h3>Example: Gasoline Tax<\/h3>\nA gasoline tax is a flat tax when considered in terms of consumption. A tax of, say, $0.30 per gallon is proportional to the amount of gasoline purchased. Someone buying 10 gallons of gas at $4 a gallon would pay $3 in tax, which is $3\/$40 = 7.5%. Someone buying 30 gallons of gas at $4 a gallon would pay $9 in tax, which is $9\/$120 = 7.5%, the same effective rate.\n\nHowever, in terms of income, a gasoline tax is often considered a regressive tax. It is likely that someone earning $30,000 a year and someone earning $60,000 a year will drive about the same amount. If both pay $60 in gasoline taxes over a year, the person earning $30,000 has paid 0.2% of their income, while the person earning $60,000 has paid 0.1% of their income in gas taxes.\n\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\nA sales tax is a fixed percentage tax on a person\u2019s purchases. Is this a flat, progressive, or regressive tax?\n\n[practice-area rows=\"4\"][\/practice-area]\n[reveal-answer q=\"807267\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"807267\"]<p>While sales tax is a flat percentage rate, it is often considered a regressive tax for the same reasons as the gasoline tax.<\/p>[\/hidden-answer]\n\n[ohm_question]65941[\/ohm_question]\n\n<\/div>\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate sales and income taxes&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:7041,&quot;3&quot;:{&quot;1&quot;:0},&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Calculate sales and income taxes<\/span><\/li>\n<\/ul>\n<\/div>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/27192407\/5120304358_f64b93a2ec_o.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2212 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/27192407\/5120304358_f64b93a2ec_o-300x212.jpg\" alt=\"magnifying lens over the word &quot;tax&quot;\" width=\"442\" height=\"312\" \/><\/a><\/p>\n<p>Governments collect taxes to pay for the services they provide. In the United States, federal income taxes help fund the military, the environmental protection agency, and thousands of other programs. Property taxes help fund schools. Gasoline taxes help pay for road improvements. While very few people enjoy paying taxes, they are necessary to pay for the services we all depend upon.<\/p>\n<p>Taxes can be computed in a variety of ways, but are typically computed as a percentage of a sale, of one\u2019s income, or of one\u2019s assets.<\/p>\n<div class=\"textbox examples\">\n<h3>recall calculations with percents<\/h3>\n<p>To make calculations using percents, first convert the percent to a decimal by dropping the % symbol and moving the decimal two places to the left (adding more zeros to the left as needed).<\/p>\n<p>Ex. Write 2.7% as a decimal<\/p>\n<p>Write 02.7 then move the decimal two places left to divide by 100.<\/p>\n<p>0.027 is the decimal representation of 2.7%.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Sales Tax<\/h3>\n<p>The sales tax rate in a city is 9.3%. How much sales tax will you pay on a $140 purchase?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q620729\">Show Solution<\/span><\/p>\n<div id=\"q620729\" class=\"hidden-answer\" style=\"display: none\">\n<p>The sales tax will be 9.3% of $140. To compute this, we multiply $140 by the percent written as a decimal: $140(0.093) = $13.02.<\/p>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"ohm80109\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=80109&theme=oea&iframe_resize_id=ohm80109&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>When taxes are not given as a fixed percentage rate, sometimes it is necessary to calculate the <strong>effective tax rate<\/strong>:<strong>&nbsp;<\/strong>the equivalent percent rate of the tax paid out of the dollar amount the tax is based on.<\/p>\n<div class=\"textbox examples\">\n<h3>Write a ratio as a percent<\/h3>\n<p>To obtain a percent from a ratio, divide the part by the whole and multiply by 100.<\/p>\n<p>Ex. If 87 out of 932 people polled claim to dislike pizza, the percent of people polled who stated they don&#8217;t like pizza is:<\/p>\n<p>[latex]\\dfrac{\\text{ part }}{\\text{ whole }}=\\dfrac{87}{932} \\approx .0934[\/latex]<\/p>\n<p>[latex].0934 \\cdot 100 = 9.34 \\%[\/latex].<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Property Tax<\/h3>\n<p>Jaquim&nbsp;paid $3,200 in property taxes on his&nbsp;house valued at $215,000 last year. What is the effective tax rate?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q696377\">Show Solution<\/span><\/p>\n<div id=\"q696377\" class=\"hidden-answer\" style=\"display: none\">\n<p>We can compute the equivalent percentage: 3200\/215000 = 0.01488, or about 1.49% effective rate.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Taxes are often referred to as progressive, regressive, or flat.<\/p>\n<ul>\n<li>A <strong>flat tax<\/strong>, or proportional tax, charges a constant percentage rate.<\/li>\n<li>A <strong>progressive tax<\/strong> increases the percent rate as the base amount increases.<\/li>\n<li>A <strong>regressive tax <\/strong>decreases the percent rate as the base amount increases.<\/li>\n<\/ul>\n<div class=\"textbox exercises\">\n<h3>Example: Federal Income Tax<\/h3>\n<p>The United States federal income tax on earned wages is an example of a progressive tax. People with a higher wage income pay a higher percent tax on their income.<\/p>\n<p>For a single person in 2011, adjusted gross income (income after deductions) under $8,500 was taxed at 10%. Income over $8,500 but under $34,500 was taxed at 15%.<\/p>\n<h4>Earning $10,000<\/h4>\n<p>Stephen earned&nbsp;$10,000 in 2011. He would pay 10% on the portion of his&nbsp;income under $8,500, and 15% on the income over $8,500.<\/p>\n<p>8500(0.10) = 850 &nbsp; &nbsp; 10% of $8500<br \/>\n1500(0.15) = 225 &nbsp; &nbsp; &nbsp;15% of the remaining $1500 of income<br \/>\nTotal tax:&nbsp;&nbsp; = $1075<\/p>\n<p>What was Stephen&#8217;s effective tax rate?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q696772\">Show Solution<\/span><\/p>\n<div id=\"q696772\" class=\"hidden-answer\" style=\"display: none\">\n<p>The effective tax rate paid is 1075\/10000 = 10.75%<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h4>Earning $30,000<\/h4>\n<p>D&#8217;Andrea&nbsp;earned $30,000 in 2011. She would also pay 10% on the portion of her&nbsp;income under $8,500, and 15% on the income over $8,500.<\/p>\n<p>8500(0.10) = 850&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 10% of $8500<br \/>\n21500(0.15) = 3225&nbsp;&nbsp;&nbsp; 15% of the remaining $21500 of income<br \/>\nTotal tax:&nbsp;&nbsp; = $4075<\/p>\n<p>What was D&#8217;Andrea&#8217;s effective tax rate?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q648795\">Show Solution<\/span><\/p>\n<div id=\"q648795\" class=\"hidden-answer\" style=\"display: none\">\n<p>The effective tax rate paid is 4075\/30000 = 13.58%.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Notice that the effective rate has increased with income, showing this is a progressive tax.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example: Gasoline Tax<\/h3>\n<p>A gasoline tax is a flat tax when considered in terms of consumption. A tax of, say, $0.30 per gallon is proportional to the amount of gasoline purchased. Someone buying 10 gallons of gas at $4 a gallon would pay $3 in tax, which is $3\/$40 = 7.5%. Someone buying 30 gallons of gas at $4 a gallon would pay $9 in tax, which is $9\/$120 = 7.5%, the same effective rate.<\/p>\n<p>However, in terms of income, a gasoline tax is often considered a regressive tax. It is likely that someone earning $30,000 a year and someone earning $60,000 a year will drive about the same amount. If both pay $60 in gasoline taxes over a year, the person earning $30,000 has paid 0.2% of their income, while the person earning $60,000 has paid 0.1% of their income in gas taxes.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>A sales tax is a fixed percentage tax on a person\u2019s purchases. Is this a flat, progressive, or regressive tax?<\/p>\n<p><textarea aria-label=\"Your Answer\" rows=\"4\"><\/textarea><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q807267\">Show Solution<\/span><\/p>\n<div id=\"q807267\" class=\"hidden-answer\" style=\"display: none\">\n<p>While sales tax is a flat percentage rate, it is often considered a regressive tax for the same reasons as the gasoline tax.<\/p>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"ohm65941\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=65941&theme=oea&iframe_resize_id=ohm65941&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4638\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Problem Solving. <strong>Authored by<\/strong>: David Lippman. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li><strong>Authored by<\/strong>: Calita Kabir. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/flic.kr\/p\/8NsU6C\">https:\/\/flic.kr\/p\/8NsU6C<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID 65951. <strong>Authored by<\/strong>: Parker,Gary. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li>Question ID 80109. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t 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