Assignment 5: Algebra Problems

For this assignment, you will be working on problems from
Chapter 3 of *Problem Solving Through Recreational Mathematics*,
as discussed below, but first, some announcements...

The first Math/CS colloquium of the semester will take place on Wednesday, February 13, at 4:30 PM in Napier 201. Refreshments will be available at 4:00 in Napier 218. Hobart alum Vince Cassano '91 and William Smith alum Kim Oaks '85 will discuss what it's like to be an actuary. Remember that you are required to attend at least one Math/CS colloquium this term. An attendance sheet will be available at the talk. (There won't be room for everyone to attend the same talk; there will be more opportunities later in the term.)

Dave Brown, the math intern, is modifying his hours. You should have gotten an email about this. Dave is available in Lansing 310 to offer math help to students in 100-level courses.

Finally, note that there is a **test** next Friday, February 22.

For this assignment, you should work in groups of three. (There will be
one group of four, if everyone is there.) The problems that you will work on
are algebra word problems from Chapter 3 of *Problem Solving Through
Recreational Mathematics*. Your **main** task is to develop equations
that represent the information in each problem. Of course, you should also
try to solve the equations to get a solution to the problem, but the main skill
that I am interested in is the ability to translate an English description
of a problem into algebraic form.

For each problem, you should introduce one or more variables to represent one or
more unknown quantities. You should state clearly what each variable
represents. Then translate the information in the problem into one or
more equations. Describe, in full English sentences, what each equation
means and how it relates to the problem as originally stated. You might want
to discuss the reasoning you did to come up with the equations, if it isn't
obvious. Then, try
to solve the equations. *Show your work.* Be sure to make it clear how
any numbers that you come up with relate to the specific question that was
asked in the problem; that is, state your answer to the question in a full
English sentence.

Do the following problems, which can be found on pages 84 through 96: 3.3, 3.13, 3.35, 3.47, 3.50, 3.63, and 3.64.

The assignment will be due in class next Wednesday. You will have some additional time to work on the problems in class on Friday or Monday. Note that one of the problems (3.35) involves "uniform motion," and for that problem you need to remember the rule that "speed equals distance over time" or "distance equals speed times time". Three of the problems (3.47, 3.50, and 3.63) are "work" problems; when doing work problems, you usually want to use variables to represent the amount of work or fraction of work done by a worker in a unit time ("work per worker per time unit"). Problem 3.13 needs two variables and two equations, while 3.3 and 3.64 can be done with one variable and one equation. Note that problems 3.63 and 3.64 are taken from a 1500-year old collection of math problems, which shows that for at least that long, people have been enjoying such problems -- or maybe that teachers have been inflicting such problems on their students.