Technical Mathematics, Sixth Edition

3.4. Money Problems

Our next group of applications is in an area that concerns us all, on the job and especially in our private lives: money.

We usually work financial problems to the nearest dollar or nearest penny, regardless of the significant digits in the original numbers.

Example 30: A consultant had to pay income taxes of $4867 plus 15% of the amount by which her taxable income exceeded $32,450. Her tax bill was $12,386. What was her taxable income? Work to the nearest dollar. Solution: Let x = taxable income (dollars). The amount by which her income exceeded $32,450 is then x − 32,450 Her tax is 15% of that amount, plus $4867, so tax = 4867 + 0.15(x − 32,450) = 12,386 Solving for x we get Check: Her income exceeds $32,450 by ($82,577 − $32,450) or $50,127. A 15% tax on that amount is 0.15($50,127) or $7,519. Her total tax is then $7,159 + $4867 or $12,386, as required.

Example 31: A person invests part of his $10,000 savings in a bank, at 6%, and part in a certificate of deposit, at 8%, both simple interest. He gets a total of $750 per year in interest from the two investments. How much is invested at each rate? Solution: We first define our variables. Let x = amount invested at 6% and 10,000 − x = amount invested at 8% If x dollars are invested at 6%, the interest on that investment is 0.06x dollars. Similarly, 0.08(10,000 − x) dollars are earned on the other investment. ...