TPC Functions Course Fall 2005

Pat Thompson/Marilyn Carlson

The following problems are from an algebra text. If you approach them traditionally, you will write an equation and solve for the variable in that equation. As you noted earlier, in writing this equation you will be treating the variable as if it is a constant—it does not vary. Rather, it stands for “the answer”. As such:

a) How can we think of this problem so that it involves a functional relationship between covarying quantities?

b) How can we phrase the problem's question so that the answer is a function?

c) What additional question can we ask so that the answer to it is an answer to the original question?

d) What additional questions would be helpful, useful, or otherwise potentially illuminating?

16. Amy is paid time-and-a-half for hours worked in excess of 40 hours and double-time for hours worked on Sunday. If Amy had gross weekly wages of $342 for working 50 hours, 4 of which were on Sunday, what is her regular hourly rate?

23. Lauren, a recent retiree, requires $6000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 15% per year or in a Certificate of Deposit (CD) paying 7% per year. How much money should be invested in each to realize exactly $6000 in interest per year? [Ignore the fact that any sane person would put everything into the B-rated bonds.]

27. The area of the opening of a rectangular window is to be 143 square feet. If the length is to be 2 feet more than the width, what are the dimensions?

31. An open box is to be constructed from a square piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should be the dimensions of the sheet metal?

39. Craig can deliver his newspapers in 30 minutes. It takes Jim 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?