Week 2
Written Assignment 1

Answer the following questions. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. Use Equation Editor to write mathematical expressions and equations. Show your work (calculations and explanation) for every problem. The credit will not be given if work is not shown.

Problem #1 (10 points)
Business and finance. The cost, in dollars, of typing a term paper is given as
3 times the number of pages plus 20. Use y as the number of pages to be typed and write a polynomial to describe this cost. Find the cost of typing a 50-page paper.

The cost of typing a paper with y pages is P.

Therefore, P = 3y + 20

Substituting y = 50,

P = 3(50) + 20
P = 150 + 20
P = 170

Therefore it would cost $170 to type a 50-page paper.

Problem #2 (10 points)
Geometry. If the sides of a square are decreased by 2 cm, the area is decreased by
36 cm2. What were the dimensions of the original square?

Area of a square = s*s, where s is the length of a side.
We know from the question that: s2 - 36 = (s - 2)(s - 2) s2 = s2 - 4s + 4 + 36
4s = 40 s = 10

Therefore the dimensions of the original square are 10 by 10.

Problem #3 (10 points)
Business and finance. The relationship between the number of calculators x that a company can sell per month and the price of each calculator p is given by x = 1700 - 100p. Find the price at which a calculator should be sold to produce a monthly revenue of $7000. (Hint: Revenue = xp.)

xp = 7000 p = 7000/x

Sub this in:

x = 1700 - 100(7000/x) x = 1700 - 700000/x x2 = 1700x - 700000 x2 - 1700x + 700000 = 0

Solving this gives you x =700, sub that in, 7000 = 700(p), therefore P = $10.

ACTIVITY 1: ISBNS AND THE CHECK DIGIT (20 points)

This activity is designed to enhance your understanding of the topics of these chapters, and to provide you with a mathematical extension of topics we have covered. For material related to this activity, visit the text website at www.mhhe.com/streeter.

Have you ever noticed the long number, usually accompanied by a bar code, that can be found on the back of a book? This is called the International Standard Book Number (ISBN). Each book has a unique ISBN, which is 10 digits in length. The most common form for an ISBN is X-XX-XXXXXX-X. Each ISBN has four blocks of digits.

• The first block of digits on the left represents the language of the book (0 is used to represent
English). This block is usually one digit in length.
• The second block of digits represents the publisher. This block is usually two or three digits in length.
• The third block of digits represents the number assigned to the book by the publishing company. This is usually five or six digits in length.
• The fourth block consists of the check digit.

For the purposes of this document, we will consider the ISBN 0-07-229654-2.
The digit of most interest is the final digit, the check digit. When an ISBN is entered into a computer, the computer looks at the check digit to make certain that the numbers were properly entered. We will look at the algorithm used to generate the check digit.

Activity
I. To determine the check digit for the ISBN of a text, follow these steps.

1. Multiply each of the nine assigned digits by a weighted value. The weighted values are 1 for the first digit from the left, 2 for the second digit, 3 for third digit, etc. In our case, we have

1 • 0 + 2 • 0 + 3 • 7 + 4 • 2 + 5 • 2 + 6 • 9 + 7 • 6 + 8 • 5 + 9 • 4 = 211

2. In mathematics, we occasionally are interested in only the remainder after we do division. We refer to the remainder as the modular (or mod) of the divisor. The ISBN uses (mod 11) to determine the check digit.

211 ÷ 11 = 19 with a remainder of 2. We say 211 = 2 (mod 11)
That is how we get the 2 in the ISBN 0-07-229654-2.

II. If we are given an ISBN and we want to check its validity, we can follow a similar algorithm. 1. Multiply each of the 10 digits by a weighted value. The weighted values are still 1 for the first digit from the left, 2 for the second digit, etc., but we also multiply 10 times the tenth (check) digit.
In our case, we now have

1 • 0 + 2 • 0 + 3 • 7 + 4 • 2 + 5 • 2 + 6 • 9 + 7 • 6 + 8 • 5 + 9 • 4 + 10 • 2 = 231

2. For any valid ISBN, the result will have a remainder of zero when divided by 11. In other words, we will have 0 (mod 11). Note that 231 ÷ 11 = 21.

Determine whether each of the following is a valid ISBN.

0-07-038023-6

1×0 + 2×0 + 3×7 + 4×0 + 5×3 + 6×8 + 7×0 + 8×2 + 9×3 + 10× 6
0 + 0 + 21 + 0 + 15 + 48 + 0 + 16 + 27 + 60 = 187

187÷11= 17

187 is divisible by 11, therefore this is a valid ISBN.

0-15-249584-2

1×0 + 2×1 + 3×5 + 4×2 + 5×4 + 6×9 + 7×5 + 8×8 + 9×4 + 10×2
0 + 2 + 15 + 8 + 20 + 54 + 35 + 64 + 36 + 20 = 254

254÷11= 23.0909

254 is not divisible by 11, therefore this is not a valid ISBN.

0-553-34948-1

1×0 + 2×5 + 3×5 + 4×3 + 5×3 + 6×4 + 7×9 + 8×4 + 9×8 + 10×1
0 + 10 + 15 + 12 + 15 + 24 + 63 + 32 + 72 + 10 = 253

253÷11= 23

253 is divisible by 11, therefore this is a valid ISBN.

0-07-000317-3

1×0 + 2×0 + 3×7 + 4×0 + 5×0 + 6×0 + 7×3 + 8×1 + 9×7 + 10×3
0 + 0 + 21 + 0 + 0 + 0 + 21 + 8 + 63 + 30 = 143

143÷11= 13

143 is divisible by 11, therefore this is a valid ISBN.

For those numbers above that are valid, go on-line and find the books to which they refer.

0-07-038023-6: 3000 Solved Problems in Linear Algebra
By: Seymour Lipshultz

0-553-34948-1: Another Roadside Attraction
By: Tom Robbins

0-07-000317-3: Wines of America
By: Leon D. Adams