Algebra Know-It-ALL

These worked-out solutions do not necessarily represent the only way a problem can be fig-

ured out. If you think you can solve a particular problem in a quicker or better way than you

see here, by all means go ahead! But always check your work to be sure your “alternative”

answer is correct.

Chapter 1

1. There are several ways to figure this out, but they’re all a little “messy.” You can count
   the days out loud and write “hash marks” on a sheet of paper, or you can use a calendar
   and write numerals on it day by day, starting with 0 on June 24 and working up. If you
   want to avoid all that counting, you can figure out the number of days of interest in
   June, July, August, September, and October, and then add them up. Remember that
   in any year, June has 30 days, July has 31 days, August has 31 days, and September has
   30 days. In June, you have 30 − 24 = 6 days of interest; in July you have all 31 days; in
   August you have all 31 days; in September you have all 30 days; in October you have
   2 days of interest. The total is therefore 6 + 31 + 31 + 30 + 2 = 100 days.


2. Remember that 1 = I, 5 = V, 10 = X, 50 = L, and 100 = C. The answers are as follows,
   broken down into sums for clarification.
   (a) 200 = 100 + 100 = C + C = CC
   (b) 201 = 100 + 100 + 1 = C + C + I = CCI
   (c) 209 = 100 + 100 + 9 = C + C + IX = CCIX
   (d) 210 = 100 + 100 + 10 = C + C + X = CCX


3. Remember that M = 1,000, C = 100, X = 10, V = 5, and I = 1. The answers are as
   follows, broken down into sums for clarification.
   (a) MMXX = 1,000 + 1,000 + 10 + 10 = 2,020
   (b) MMXIX = 1,000 + 1,000 + 10 + 9 = 2,019

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APPENDIX

A

Worked-Out Solutions to

Appendix A Worked-Out Solutions to Exercises: Chapters 1 to

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