{"id":84,"date":"2023-02-01T00:03:08","date_gmt":"2023-02-01T00:03:08","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/putting-it-together-general-problem-solving-2\/"},"modified":"2023-04-02T23:10:27","modified_gmt":"2023-04-02T23:10:27","slug":"putting-it-together-general-problem-solving-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/putting-it-together-general-problem-solving-2\/","title":{"raw":"Putting It Together: Problem Solving and Proportional Reasoning","rendered":"Putting It Together: Problem Solving and Proportional Reasoning"},"content":{"raw":"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. \u00a0In real life, sometimes we have to make big decisions. \u00a0A 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.\r\n\r\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\" \/>\r\n\r\n&nbsp;\r\n\r\nSuppose you are currently working as a bank teller in your hometown. \u00a0Your job pays $11 per hour, with 10% taxes taken out of each paycheck. \u00a0For simplicity, assume you have to work 260 days of the year (you don\u2019t work weekends), 8 hours a day. \u00a0By carefully budgeting you can keep you monthly expenses to about $1500.\r\n\r\nBut now another job offer has come up. \u00a0You have the opportunity to become an assistant manager. \u00a0The only catch is that you\u2019ll have to move to a new branch of the bank opening up in a nearby metropolitan area. \u00a0So here are the details:\r\n\r\nThe assistant manager salary starts at $32,000. \u00a0This puts you into the next tax bracket, which means that you will pay $2500 plus 15% of the amount earned over $25,000. \u00a0Because you are moving to a bigger city, your living expenses will rise as well. \u00a0After a little research, you determine that your monthly expenses will probably be around $2000.\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\"><strong><em>Should you make the move and take the job offer?<\/em><\/strong><\/p>\r\n&nbsp;\r\n\r\nThis is a tough decision! \u00a0We should do some calculations first. \u00a0How much money do you make in a full year as a bank teller? \u00a0First let\u2019s find out how many total hours you work in a year.\r\n<p style=\"padding-left: 30px;\">[latex]8 \\; \\textrm{hrs.}\/\\textrm{day} \\times 260 \\;\\textrm{days} = 2080 \\;\\textrm{hrs.}[\/latex]<\/p>\r\nNext, multiply by the hourly wage to determine your <strong>gross income<\/strong>.\r\n<p style=\"padding-left: 30px;\">[latex]2080 \\;\\textrm{hrs.}\\times 11 \\; \\$ \/ \\textrm{hr.} = \\$22,\\!880[\/latex]<\/p>\r\nBut don\u2019t forget about taxes! \u00a0You will have to pay 10% (or 0.10) of this amount to the US government.\r\n<p style=\"padding-left: 30px;\">[latex]$22,880\\times0.10=$2288[\/latex]<\/p>\r\nAfter subtracting the tax, this leaves you with your <strong>net income<\/strong>, or <strong>take-home pay<\/strong>:\r\n<p style=\"padding-left: 30px;\">[latex]$22,880-$2288=$20,592[\/latex]<\/p>\r\nOk, so now let\u2019s figure out the yearly expenses. \u00a0If monthly expenses are $1500, then each year you will pay:\r\n<p style=\"text-align: left; padding-left: 30px;\">[latex]12\\times$1500=$18,000[\/latex]<\/p>\r\nFinally, after the bills are paid, you can do what we want to with the remainder. \u00a0This is our <strong>discretionary budget<\/strong>, and it is as good a measure as any as to how successful you are.\r\n<p style=\"text-align: left; padding-left: 30px;\">[latex]\\$20,\\!592 - \\$18,\\!000 = \\$2592[\/latex]<\/p>\r\n&nbsp;\r\n\r\nNow keep that number $2592 in mind. \u00a0Let\u2019s see what kind of discretionary budget you will have if you take the new job. \u00a0Since salary is, by definition, a yearly income amount, our first task is to compute and deduct the taxes. \u00a0This time, you will pay $2500 plus 15% of the difference between the salary and $25,000.\r\n<p style=\"text-align: left; padding-left: 30px;\">[latex]$2500+($7000\\times0.15)=$3550[\/latex]<\/p>\r\nTherefore, the net income would be:\r\n<p style=\"text-align: left; padding-left: 30px;\">[latex]$32,000-$3550=$28,450[\/latex]<\/p>\r\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? \u00a0Take the estimated monthly expenses of $2000 and multiply it by 12 months:\r\n<p style=\"text-align: left; padding-left: 30px;\">[latex]12\\times$2000=$24,000[\/latex]<\/p>\r\nThus your new discretionary budget would be:\r\n<p style=\"text-align: left; padding-left: 30px;\">[latex]$28,450-$24,000=$4450[\/latex]<\/p>\r\n&nbsp;\r\n\r\nThat\u2019s definitely an improvement over $2592. \u00a0Maybe it\u2019s time to move to the big city and start advancing your career. \u00a0However, you can see that it\u2019s not really that much more, so you probably shouldn\u2019t go out and buy a brand new car. \u00a0Just wait until you get your first promotion to full manager.\r\n\r\n&nbsp;","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. \u00a0In real life, sometimes we have to make big decisions. \u00a0A 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. \u00a0Your job pays $11 per hour, with 10% taxes taken out of each paycheck. \u00a0For simplicity, assume you have to work 260 days of the year (you don\u2019t work weekends), 8 hours a day. \u00a0By carefully budgeting you can keep you monthly expenses to about $1500.<\/p>\n<p>But now another job offer has come up. \u00a0You have the opportunity to become an assistant manager. \u00a0The only catch is that you\u2019ll have to move to a new branch of the bank opening up in a nearby metropolitan area. \u00a0So here are the details:<\/p>\n<p>The assistant manager salary starts at $32,000. \u00a0This puts you into the next tax bracket, which means that you will pay $2500 plus 15% of the amount earned over $25,000. \u00a0Because you are moving to a bigger city, your living expenses will rise as well. \u00a0After a little research, you determine that your monthly expenses will probably be around $2000.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong><em>Should you make the move and take the job offer?<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>This is a tough decision! \u00a0We should do some calculations first. \u00a0How much money do you make in a full year as a bank teller? \u00a0First let\u2019s find out how many total hours you work in a year.<\/p>\n<p style=\"padding-left: 30px;\">[latex]8 \\; \\textrm{hrs.}\/\\textrm{day} \\times 260 \\;\\textrm{days} = 2080 \\;\\textrm{hrs.}[\/latex]<\/p>\n<p>Next, multiply by the hourly wage to determine your <strong>gross income<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">[latex]2080 \\;\\textrm{hrs.}\\times 11 \\; \\$ \/ \\textrm{hr.} = \\$22,\\!880[\/latex]<\/p>\n<p>But don\u2019t forget about taxes! \u00a0You 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. \u00a0If 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. \u00a0This 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. \u00a0Let\u2019s see what kind of discretionary budget you will have if you take the new job. \u00a0Since salary is, by definition, a yearly income amount, our first task is to compute and deduct the taxes. \u00a0This 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? \u00a0Take 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. \u00a0Maybe it\u2019s time to move to the big city and start advancing your career. \u00a0However, you can see that it\u2019s not really that much more, so you probably shouldn\u2019t go out and buy a brand new car. \u00a0Just 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-84\">\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":678587,"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-84","chapter","type-chapter","status-publish","hentry"],"part":64,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/84","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/users\/678587"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/84\/revisions"}],"predecessor-version":[{"id":3274,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/84\/revisions\/3274"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/parts\/64"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/84\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/media?parent=84"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=84"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/contributor?post=84"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/license?post=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}