Fun with Fundamentals: Problem 178

Seaming contradiction

Problem 178 — The whole is not always the sum of the parts, as this month’s problem by A. Towndrow of Ft. Pierce, Fla., demonstrates.

“Why certainly, sir. It’ll be no problem,” chirped Lucius Bluff on the phone. “Special orders are the Lee Key Hydraulic Company’s specialty!”

At the other end of the phone Percy McTwipp sniffed. “I certainly do not need another episode like the one I had with my titanium triangle! All right. You’ll receive four squared 48 × 96-in. 10-gauge metal sheets from me, and I’ll expect my elliptical tank with flat, seamless ends in six weeks. Remember, it must hold at least 650 gal. Good day!”

Bluff had the tank built to a true elliptical shape with only two shell seams. Neglect the thickness of the sheets. What, approximately, is the largest-capacity, enclosed, elliptical tank with flat, seamless ends that can be built with the four metal sheets? Will McTwipp get his money’s worth?

Technical consultant: Jack Couillard, Menasha, Wis.

Solution to last month’s problem 177 — You can put your money where your mouth is, if you answered $15. Here’s how McSnead’s day went:

Let x 5 amount of money McSnead started out with, dollars

The amount he gave his wife is:

The amount he had leftover is:

This amount is $1. Therefore, z = $3.

Plug the value for z into (2) to get y= 7. Plug the value for y into (1) to get x= 15.

McSnead had better brown-bag it for awhile!

Contest winner — Congratulations to Gerald Schichtel of Elmira, N.Y., who won our September contest by having his name drawn from the 43 contestants who answered correctly 7.64 sec for the first part and 9.55 for the second out of a total of 48 for that month. A TI-68 calculator is in the mail to him.

The TI-68 Advanced Scientific Calculator by Texas Instruments can solve five simultaneous equations with real and complex coefficients and has 40 number functions that can be used in both the rectangular and polar coordinate systems. Other functions include formula programming, integration, and polynomial root finding. The calculator also features a last-equation replay function that lets you double-check your work.