4th ed word translations pg 136

[sachin.w]

Begin by considering the extreme case in which each guest eats as much food as possible, or
2.5 pounds apiece. The corresponding number of guests at the banquet works out to
401/2.5 = 160.4 people.
However, you obviously cannot have a fractional number of guests at the banquet. Thus the
answer must be rounded. To determine whether to round up or down, consider the explicit
constraint: the amount of food per guest is a maximum of 2.5 pounds per guest. Therefore,
the minimum number of guests is 160.4 (if guests could be fractional), and we must round
up to make the number of guests an integer: 161.
Note the careful reasoning required! Although the phrase "minimum number of guests" may
tempt you to round down, you will get an incorrect answer if you do so. In general, as you
solve this sort of problem, put the extreme case into the underlying equation, and solve.
Then round appropriately.

I dint understand why we should round 'up' tp 161 and not 160. Please help.

[tim]

can you get 160 by adhering to the constraints of the problem? can you get 161? this is not an issue of how to round; knowing which way to round will follow naturally from an understanding of what's actually at work in this problem..

[sachin.w]

Ok. I get it now. . Thanks Tim

[tim]

cool!

[BernardK777]

Is the reason rounding up to 161 is not possible because (2.5) x (161) > 401?

[RonPurewal]

Where is the actual problem?

Please post the actual text of the problem itself. Thanks.

[BernardK777]

Chapter 7: Extra Problem Types (79 / 100 online version)

"The guests at a football banquet consumed a total of 401 pounds of food. If no individual guest consumed more than 2.5 pounds of food, what is the minimum number of guests that could have attended the banquet"

No answer choices provided.

[tim]

Please read my previous post. This is not a question about rounding; it's a question of finding the optimal integer that works. If you solve the straight algebra problem and get a number between 160 and 161, you have to analyze what happens at 160 and at 161 (which it looks like you sort of did) to decide which one barely works and which one doesn't. Do not "round" anything though!

[RonPurewal]

If I need exactly 19.001 pounds of something that comes in one-pound packages, I'm going to have to buy twenty packages.

[BernardK777]

Tim,

After reading your previous post, I am still unsure of what your intuition was for choosing 160 versus 161. Can you explain further? Was my reasoning that "161 is not possible because (2.5) x (161) > 401" and therefore does not adhere to the constraints not sound?

Thanks.

[jnelson0612]

Tim,

After reading your previous post, I am still unsure of what your intuition was for choosing 160 versus 161. Can you explain further? Was my reasoning that "161 is not possible because (2.5) x (161) > 401" and therefore does not adhere to the constraints not sound?

Thanks.

Hi Bernard,
The question is what is the minimum number of guests that I can have at the party?

Here's what I know:
No one ate more than 2.5 pounds of food
401 pounds of food were consumed

Let's try 160 guests first. If I have 160 guests, and everyone eats the maximum possible amount of food (2.5 pounds, because it says that no one ate more than that), then 160 * 2.5 = 400. Wait, the problem says that the guests ate 401 pounds of food; thus, I need at least one more guest. I need to have a minimum of 161 guests. I do think that your reasoning was going in the right direction.

[RonPurewal]

^^ Thinking about these kinds of constraints with common sense is pretty straightforward.
Thinking about them without common sense (i.e., trying to memorize "rules" for them) is pretty much impossible.