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Study Guides > Math for Liberal Arts: Co-requisite Course

Putting It Together: General Problem Solving

Now that you have seen a number of general problem solving techniques and plenty of examples in this module, let’s try to put it all together.  In real life, sometimes we have to make big decisions.  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. Green sign with words   Suppose you are currently working as a bank teller in your hometown.  Your job pays $11 per hour, with 10% taxes taken out of each paycheck.  For simplicity, assume you have to work 260 days of the year (you don’t work weekends), 8 hours a day.  By carefully budgeting you can keep you monthly expenses to about $1500. But now another job offer has come up.  You have the opportunity to become an assistant manager.  The only catch is that you’ll have to move to a new branch of the bank opening up in a nearby metropolitan area.  So here are the details: The assistant manager salary starts at $32,000.  This puts you into the next tax bracket, which means that you will pay $2500 plus 15% of the amount earned over $25,000.  Because you are moving to a bigger city, your living expenses will rise as well.  After a little research, you determine that your monthly expenses will probably be around $2000.  

Should you make the move and take the job offer?

  This is a tough decision!  We should do some calculations first.  How much money do you make in a full year as a bank teller?  First let’s find out how many total hours you work in a year.

[latex]8 \; \textrm{hrs.}/\textrm{day} \times 260 \;\textrm{days} = 2080 \;\textrm{hrs.}[/latex]

Next, multiply by the hourly wage to determine your gross income.

[latex]2080 \;\textrm{hrs.}\times 11 \; \$ / \textrm{hr.} = \$22,\!880[/latex]

But don’t forget about taxes!  You will have to pay 10% (or 0.10) of this amount to the US government.


After subtracting the tax, this leaves you with your net income, or take-home pay:


Ok, so now let’s figure out the yearly expenses.  If monthly expenses are $1500, then each year you will pay:


Finally, after the bills are paid, you can do what we want to with the remainder.  This is our discretionary budget, and it is as good a measure as any as to how successful you are.

[latex]\$20,\!592 - \$18,\!000 = \$2592[/latex]

  Now keep that number $2592 in mind.  Let’s see what kind of discretionary budget you will have if you take the new job.  Since salary is, by definition, a yearly income amount, our first task is to compute and deduct the taxes.  This time, you will pay $2500 plus 15% of the difference between the salary and $25,000.


Therefore, the net income would be:


It’s 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?  Take the estimated monthly expenses of $2000 and multiply it by 12 months:


Thus your new discretionary budget would be:


  That’s definitely an improvement over $2592.  Maybe it’s time to move to the big city and start advancing your career.  However, you can see that it’s not really that much more, so you probably shouldn’t go out and buy a brand new car.  Just wait until you get your first promotion to full manager.  

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