{"id":4639,"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-2\/"},"modified":"2020-04-21T00:19:13","modified_gmt":"2020-04-21T00:19:13","slug":"putting-it-together-general-problem-solving-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/putting-it-together-general-problem-solving-2\/","title":{"raw":"Putting It Together: General Problem Solving","rendered":"Putting It Together: General Problem Solving"},"content":{"raw":"\nNow that you have seen a number of general problem solving techniques and plenty of examples in this module, let\u2019s try to put it all together. &nbsp;In real life, sometimes we have to make big decisions. &nbsp;A major career change or relocation can throw your life into disarray, but perhaps even more importantly, such a change can have lasting effects on your financial future.\n\n<img class=\"aligncenter wp-image-294\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/4914\/2019\/12\/17155432\/budget-for-new-ideas.jpg\" alt=\"Graphic of balance scale with stack of bills on one side and a lightbulb on the other. An arm is holding the balance point.\" width=\"556\" height=\"372\">\n\n&nbsp;\n\nSuppose you are currently working as a bank teller in your hometown. &nbsp;Your job pays $11 per hour, with 10% taxes taken out of each paycheck. &nbsp;For simplicity, assume you have to work 260 days of the year (you don\u2019t work weekends), 8 hours a day. &nbsp;By carefully budgeting you can keep you monthly expenses to about $1500.\n\nBut now another job offer has come up. &nbsp;You have the opportunity to become an assistant manager. &nbsp;The only catch is that you\u2019ll have to move to a new branch of the bank opening up in a nearby metropolitan area. &nbsp;So here are the details:\n\nThe assistant manager salary starts at $32,000. &nbsp;This puts you into the next tax bracket, which means that you will pay $2500 plus 15% of the amount earned over $25,000. &nbsp;Because you are moving to a bigger city, your living expenses will rise as well. &nbsp;After a little research, you determine that your monthly expenses will probably be around $2000.\n\n&nbsp;\n<p style=\"text-align: center;\"><strong><em>Should you make the move and take the job offer?<\/em><\/strong><\/p>\n&nbsp;\n\nThis is a tough decision! &nbsp;We should do some calculations first. &nbsp;How much money do you make in a full year as a bank teller? &nbsp;First let\u2019s find out how many total hours you work in a year.\n<p style=\"padding-left: 30px;\">[latex]8 \\; \\textrm{hrs.}\/\\textrm{day} \\times 260 \\;\\textrm{days} = 2080 \\;\\textrm{hrs.}[\/latex]<\/p>\nNext, multiply by the hourly wage to determine your <strong>gross income<\/strong>.\n<p style=\"padding-left: 30px;\">[latex]2080 \\;\\textrm{hrs.}\\times 11 \\; \\$ \/ \\textrm{hr.} = \\$22,\\!880[\/latex]<\/p>\nBut don\u2019t forget about taxes! &nbsp;You will have to pay 10% (or 0.10) of this amount to the US government.\n<p style=\"padding-left: 30px;\">[latex]$22,880\\times0.10=$2288[\/latex]<\/p>\nAfter subtracting the tax, this leaves you with your <strong>net income<\/strong>, or <strong>take-home pay<\/strong>:\n<p style=\"padding-left: 30px;\">[latex]$22,880-$2288=$20,592[\/latex]<\/p>\nOk, so now let\u2019s figure out the yearly expenses. &nbsp;If monthly expenses are $1500, then each year you will pay:\n<p style=\"text-align: left; padding-left: 30px;\">[latex]12\\times$1500=$18,000[\/latex]<\/p>\nFinally, after the bills are paid, you can do what we want to with the remainder. &nbsp;This is our <strong>discretionary budget<\/strong>, and it is as good a measure as any as to how successful you are.\n<p style=\"text-align: left; padding-left: 30px;\">[latex]\\$20,\\!592 - \\$18,\\!000 = \\$2592[\/latex]<\/p>\n&nbsp;\n\nNow keep that number $2592 in mind. &nbsp;Let\u2019s see what kind of discretionary budget you will have if you take the new job. &nbsp;Since salary is, by definition, a yearly income amount, our first task is to compute and deduct the taxes. &nbsp;This time, you will pay $2500 plus 15% of the difference between the salary and $25,000.\n<p style=\"text-align: left; padding-left: 30px;\">[latex]$2500+($7000\\times0.15)=$3550[\/latex]<\/p>\nTherefore, the net income would be:\n<p style=\"text-align: left; padding-left: 30px;\">[latex]$32,000-$3550=$28,450[\/latex]<\/p>\nIt\u2019s a higher net income than you are currently making, but how will it stack up against the higher cost-of-living expenses in the city? &nbsp;Take the estimated monthly expenses of $2000 and multiply it by 12 months:\n<p style=\"text-align: left; padding-left: 30px;\">[latex]12\\times$2000=$24,000[\/latex]<\/p>\nThus your new discretionary budget would be:\n<p style=\"text-align: left; padding-left: 30px;\">[latex]$28,450-$24,000=$4450[\/latex]<\/p>\n&nbsp;\n\nThat\u2019s definitely an improvement over $2592. &nbsp;Maybe it\u2019s time to move to the big city and start advancing your career. &nbsp;However, you can see that it\u2019s not really that much more, so you probably shouldn\u2019t go out and buy a brand new car. &nbsp;Just wait until you get your first promotion to full manager.\n\n&nbsp;\n","rendered":"<p>Now that you have seen a number of general problem solving techniques and plenty of examples in this module, let\u2019s try to put it all together. &nbsp;In real life, sometimes we have to make big decisions. &nbsp;A major career change or relocation can throw your life into disarray, but perhaps even more importantly, such a change can have lasting effects on your financial future.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-294\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/4914\/2019\/12\/17155432\/budget-for-new-ideas.jpg\" alt=\"Graphic of balance scale with stack of bills on one side and a lightbulb on the other. An arm is holding the balance point.\" width=\"556\" height=\"372\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Suppose you are currently working as a bank teller in your hometown. &nbsp;Your job pays $11 per hour, with 10% taxes taken out of each paycheck. &nbsp;For simplicity, assume you have to work 260 days of the year (you don\u2019t work weekends), 8 hours a day. &nbsp;By carefully budgeting you can keep you monthly expenses to about $1500.<\/p>\n<p>But now another job offer has come up. &nbsp;You have the opportunity to become an assistant manager. &nbsp;The only catch is that you\u2019ll have to move to a new branch of the bank opening up in a nearby metropolitan area. &nbsp;So here are the details:<\/p>\n<p>The assistant manager salary starts at $32,000. &nbsp;This puts you into the next tax bracket, which means that you will pay $2500 plus 15% of the amount earned over $25,000. &nbsp;Because you are moving to a bigger city, your living expenses will rise as well. &nbsp;After a little research, you determine that your monthly expenses will probably be around $2000.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong><em>Should you make the move and take the job offer?<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>This is a tough decision! &nbsp;We should do some calculations first. &nbsp;How much money do you make in a full year as a bank teller? &nbsp;First let\u2019s find out how many total hours you work in a year.<\/p>\n<p style=\"padding-left: 30px;\">[latex]8 \\; \\textrm{hrs.}\/\\textrm{day} \\times 260 \\;\\textrm{days} = 2080 \\;\\textrm{hrs.}[\/latex]<\/p>\n<p>Next, multiply by the hourly wage to determine your <strong>gross income<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">[latex]2080 \\;\\textrm{hrs.}\\times 11 \\; \\$ \/ \\textrm{hr.} = \\$22,\\!880[\/latex]<\/p>\n<p>But don\u2019t forget about taxes! &nbsp;You will have to pay 10% (or 0.10) of this amount to the US government.<\/p>\n<p style=\"padding-left: 30px;\">[latex]$22,880\\times0.10=$2288[\/latex]<\/p>\n<p>After subtracting the tax, this leaves you with your <strong>net income<\/strong>, or <strong>take-home pay<\/strong>:<\/p>\n<p style=\"padding-left: 30px;\">[latex]$22,880-$2288=$20,592[\/latex]<\/p>\n<p>Ok, so now let\u2019s figure out the yearly expenses. &nbsp;If monthly expenses are $1500, then each year you will pay:<\/p>\n<p style=\"text-align: left; padding-left: 30px;\">[latex]12\\times$1500=$18,000[\/latex]<\/p>\n<p>Finally, after the bills are paid, you can do what we want to with the remainder. &nbsp;This is our <strong>discretionary budget<\/strong>, and it is as good a measure as any as to how successful you are.<\/p>\n<p style=\"text-align: left; padding-left: 30px;\">[latex]\\$20,\\!592 - \\$18,\\!000 = \\$2592[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>Now keep that number $2592 in mind. &nbsp;Let\u2019s see what kind of discretionary budget you will have if you take the new job. &nbsp;Since salary is, by definition, a yearly income amount, our first task is to compute and deduct the taxes. &nbsp;This time, you will pay $2500 plus 15% of the difference between the salary and $25,000.<\/p>\n<p style=\"text-align: left; padding-left: 30px;\">[latex]$2500+($7000\\times0.15)=$3550[\/latex]<\/p>\n<p>Therefore, the net income would be:<\/p>\n<p style=\"text-align: left; padding-left: 30px;\">[latex]$32,000-$3550=$28,450[\/latex]<\/p>\n<p>It\u2019s a higher net income than you are currently making, but how will it stack up against the higher cost-of-living expenses in the city? &nbsp;Take the estimated monthly expenses of $2000 and multiply it by 12 months:<\/p>\n<p style=\"text-align: left; padding-left: 30px;\">[latex]12\\times$2000=$24,000[\/latex]<\/p>\n<p>Thus your new discretionary budget would be:<\/p>\n<p style=\"text-align: left; padding-left: 30px;\">[latex]$28,450-$24,000=$4450[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>That\u2019s definitely an improvement over $2592. &nbsp;Maybe it\u2019s time to move to the big city and start advancing your career. &nbsp;However, you can see that it\u2019s not really that much more, so you probably shouldn\u2019t go out and buy a brand new car. &nbsp;Just wait until you get your first promotion to full manager.<\/p>\n<p>&nbsp;<\/p>\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-4639\">\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>Putting It Together: General Problem Solving. <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><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Budget For New Ideas. <strong>Authored by<\/strong>: mohamed mahmoud hassan. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.publicdomainpictures.net\/en\/view-image.php?image=268294&#038;picture=budget-for-new-ideas\">https:\/\/www.publicdomainpictures.net\/en\/view-image.php?image=268294&#038;picture=budget-for-new-ideas<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":20,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Putting It Together: General Problem Solving\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Budget For New Ideas\",\"author\":\"mohamed mahmoud hassan\",\"organization\":\"\",\"url\":\"https:\/\/www.publicdomainpictures.net\/en\/view-image.php?image=268294&picture=budget-for-new-ideas\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"f6f62b94-ad5f-4b95-8900-07c457e39c3f","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4639","chapter","type-chapter","status-publish","hentry"],"part":4619,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4639","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4639\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/4619"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4639\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4639"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4639"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4639"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}