Motion System Design

# Fun with Fundamentals: Problem 221

### Volume pricing

Problem 221 – The early bird doesn't always get the worm, as this month's problem by R. Kannen of King of Prussia, Pa., demonstrates.

Way up in the top shelf of Finagel J. Wurme's newly refurbished library, a book worm was eating its way through a priceless set of encyclopedia.

The set has 26 volumes, one for each letter of the alphabet. The volumes are stacked side-by-side on a shelf and arranged alphabetically from left to right starting with the letter A. The pages in each volume are printed on both sides and are numbered from 1 to 98, plus each has a front and back cover. If the worm starts on page 1 of the "A" volume and finishes through the back cover on volume "Z," how many pages and covers has it eaten through?

Solution to last month's problem 220 -- You have all your marbles if you answered: 500 for Farley and 700 for Smedley. Here's each boy's

starting position:

Let

y = Number of marbles Farley starts with.
x = Number of marbles Smedley starts with.
Farley states that if Smedley gives up 100 of his marbles, they'll each have the same. This translates into:

x - 100 = y + 100

From these we get:

x = y + 200, and
x = 2y - 300 (1)

Set both of these equal to each other:

Plugging 500 into (1), we get 700 for x.

Bluff never did find out who broke the camera!

CONTEST WINNER – Congratulations to Gerd R. Alzuhn, P.E., of Milwaukee who won our August contest by having his name drawn from the 230 contestants who answered correctly out of a total of 336 entrants for that month. A Maple V Release 5 mathematics software package is in the mail to him.

Maple V Release 5 is an interactive computer algebra system that provides a mathematical environment for manipulating symbolic algebraic expressions, arbitrary-precision numerics, graphics, and programming. Its library features over 2,700 functions that are used in many scientific and engineering applications. Features include a MATLAB link, which lets users execute MATLAB commands from inside the software; a spreadsheet function in which Maple V operations can be performed; and an HTML export function to create web pages. The software is available in Windows 95, Windows NT, Windows 3.11, Macintosh, Power Macintosh, plus UNIX and Linux platforms.

This month's problem submitter receives an EL-546L Direct Algebraic Logic calculator from Sharp Electronics. The EL-546L has an extralarge, 10-digit, two-line LCD display that lets you see the full equation on one line and the answer to the equation on the other. An algebra and playback function enables you to enter an equation and substitute numeric values or correct errors. Another feature is the full-term equation entry function, which enables the calculator to display a fraction equation exactly as it appears in a textbook. The EL-546L has dual power.

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Fun with Fundamentals: Problem 220