1. ## Algebra question

My college algebra class started this last Tuesday. We went through 85 pages of review in about 20 minutes. It's been 18 years since I've studied any math.

I think the book is wrong for the last word problem in the review. Here it is, and I show how I approached it and the answer I got.

Are you paying too much for a large pizza?
Pizza is one of the most popular foods available today, and the take-out pizza has become a staple in today's hurried world. But are you paying too much for that large pizza you ordered? Pizza sizes are typically designated by their diameters. A pizza of diameter "d" inches has an area of

PI(d/2)**2. (A.K.A. "PI-r-squared")

Let's assume that the cost of a pizza is determined by its area. Suppose a pizza parlor charges \$4.00 for a 10-inch pizza and \$9.25 for a 15-inch pizza. Evaluate the area of each pizza to show the owner that he is overcharging you by \$0.25 for the larger pizza.
So, simple enough it seems. I'll use 3.14159 for PI.

10" pizza area = 3.14159 * (10/2)**2 =
3.14159 * (5)**2 =
3.14159 * 25 = 78.53975 sq. inches.
78.53975 / \$4.00 = \$0.1963 per square inch cost.

15" pizza area = 3.14159 * (15/2)**2 =
3.14158 * (7.5)**2 =
3.14159 * 56.25 = 176.71443 sq. inches.
176.71443 / \$9.25 = \$0.1910 per square inch cost.

If the 15" pizza sells for less per sq. inch than the 10" pizza, I personally would have a hard time convincing the Red Baron he was charging \$0.25 too much.

What am I missing here?

Todd

2. Looks wrong to me, too.

3. Perhaps this is the way:

Price index of 10 inch pizza:
4 / (5 * 5 * pi) = 4 / (25 * pi)

Price of 15 inch pizza at 10 inch pizza price index:
(4 / (25 * pi)) * (7.5 * 7.5 * pi) = 9

Price difference:
9.25 - 9 = 0.25

So the larger pizza is overcharged by \$0.25

EDIT:
Oh, now it is obvious. You calculated the area per dollar. So, the more area per dollar, the better the deal. Thus the 10 inch pizza is actually cheaper per square inch than the 15 inch pizza.

4. Originally Posted by laserlight
EDIT:
Oh, now it is obvious. You calculated the area per dollar. So, the more area per dollar, the better the deal. Thus the 10 inch pizza is actually cheaper per square inch than the 15 inch pizza.
Haha! I feel kinda dumb now. Flipping ratios over == goof.

5. Son of a gun. Price index. Who'd have thunk.

Thanks Laserlight!

6. Well, perhaps I am using the term "price index" rather loosely, since it is just the ratio of price to area. Either way it works, so yeah

7. I understand my error now.

78.53975 / \$4 = 19.634... which is not the price per square inch, but the number of square inches of pizza I can buy per dollar.

So if I can only buy 19.10 square inches of pizza for a dollar for the larger pizza, it is indeed more expensive.

Thanks again!

8. Originally Posted by laserlight
Well, perhaps I am using the term "price index" rather loosely, since it is just the ratio of price to area. Either way it works, so yeah
I dislike the term "price index" because an "index" is supposed to be a dimensionless ratio, but in this case the units are "square inches per dollar." Damn those economists. The strict definition of "price index" conforms, since it's a ratio between current price and a reference price, but people commonly use it in other ways.

9. >I think the book is wrong for the last word problem in the review.
Damn straight. Everybody knows the value of a pizza is measured in pounds, not area.

10. I'd be happy to pay the extra quarter, if I can get a 6-pack out of the deal.

11. I know how you feel, I'm taking numerical analysis after about 3 years of not having taken any math.

12. I learned a "trick" last night in class. I never knew this. It has to do with multiplying by 11.

When multiplying 11 by a 2 digit or 3 digit number, you can do it in your head really quick.

let's say you have 11 * 32. Spread the 3 and the 2 apart:

3 2

Then, add the 3 and the 2 together to get 5, place it between the two number: 352. If the two middle numbers add to more than 9, add the tens digit to the left number, like this:

11 * 87

8 7

+ 15

957

For a 3 digit number, the process is similar. 11 * 345. Spread the outer two:

3 5

Now, working right to left, add 4+5

3 95

3 7 9 5 = 11 * 345

If any of the middle sums are > 9, add the tens digits to the left.

I haven't tried it, but the process would probably work with 4, 5 or more digits as well.

Todd

13. actually I just do place shifting and add, which amounts to the same thing, but reuires fewer steps. Been doing that since the 2nd grade. There are tricks like that for most of the small integers, like the easy way to tell if a number is divisible by 3 is to add up the digits ( 56421 = 5 + 6 + 4 + 2 + 1 = 18 ) if the answer is divisible by 3 then the original number is also. In this case 56421 / 3 = 18807. The same rule applies for 9 as well.

14. I don't nearly encounter as many 11s in real life as I do horrendously long real numbers or strange greek symbols which may or may not have a meaning.

15. Originally Posted by indigo0086
I don't nearly encounter as many 11s in real life as I do horrendously long real numbers or strange greek symbols which may or may not have a meaning.