Is it me or is this problem poorly written?

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bbarmann

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I'm having trouble with the following problem published by Ideal School Supply Company:

It's a fact: It takes 100 gallons of water to make a loaf of bread! Water must be used to grow and grind the wheat; to process the salt, baking powder, and any flavorings in the bread; and to add to the batter.

For each loaf of bread, the batter requires 0.5 of a gallon of water. Growing and processing the flavorings require four times the amount of water needed for grinding the wheat, which is eight times the amount of water required in the batter. How much water is needed to grow and process the flavorings? Let this number equal F. Let the amount of water needed to grind the wheat equal G. The amount of water needed to process the salt is equal to (0.25F) + 2. How much water is needed to process the salt? Let this number equal S.

How many gallons of water are required to grow the wheat for one loaf of bread?
 
Batter = .5
Grinding wheat = 4 (8 times Batter)
Flavorings = F = 16 (4 times Grinding)
Salt = F/4 + 2 = 4 + 2 = 6

Growing wheat = 100 - .5 - 4 - 16 - 6 = 73.5
 
Denis said:
Batter = .5
Grinding wheat = 4 (8 times Batter)
Flavorings = F = 16 (4 times Grinding)
Salt = F/4 + 2 = 4 + 2 = 6

Growing wheat = 100 - .5 - 4 - 16 - 6 = 73.5
Click to expand...

Denis, thank you for the response.
I think I understand your proposed answer, but I'm not satisfied that it is correct.
According to the problem, the following processes require water:
1. Growing the wheat
2. Grinding
3. Processing the salt
4. Processing baking powder
5. Processing any flavorings
6. Adding water to the batter

We are given the amount needed for the batter (.5), from which we can calculate that the amount needed for Grinding is 4 (8 x .5 = 4), and that the amount needed for Growing and Processing the flavorings (two processes combined) is 16 (4 x 4 = 16). From this last number, which we are told to call F, we can calculate the amount needed to process the salt (0.25F + 2 = 0.25(16) + 2 = 6.

If we are going to say that the total amount needed for growing wheat is 100 - the amount needed for the other processes, don't we need to know the amount for each of the processes 2-5? From the numbers above, how can we calculate how much water is needed to process the flavorings (a process separate from processing the salt), or for processing baking powder? Also, the problem says at the beginning that water is needed to grow wheat, but nothing about water needed to grow flavorings. But in the second paragraph there is a reference to "growing and processing the flavorings." It is unclear to me whether this means the amount needed to grow wheat and process the flavorings, or the amount needed to both grow and process the flavorings.
 
According to the problem, the following processes require water:
1. Growing the wheat : 100 - .5 - 4 - 16 - 6 = 73.5

2. Grinding : 4

3. Processing the salt : 6

4. Processing baking powder
and
5. Processing any flavorings : 16 (no choice but to assume these are combined.

6. Adding water to the batter : .5

That's my take on it :idea:
 
Denis said:
According to the problem, the following processes require water:
1. Growing the wheat : 100 - .5 - 4 - 16 - 6 = 73.5

2. Grinding : 4

3. Processing the salt : 6

4. Processing baking powder
and
5. Processing any flavorings : 16 (no choice but to assume these are combined.

6. Adding water to the batter : .5

That's my take on it :idea:
Click to expand...

Thank you Denis for taking the time to deal with this problem.
I see how you arrive at your answer, including the assumption that processing baking powder and flavorings are combined. But this points up to me how imprecise this question is. Why would one assume that the processing of the baking powder is combined with another step when each of these steps is called out separately in the introduction of the question? What's the point of mentioning the baking powder if you then have to assume it's combined with another step? If this was on a multiple choice test, where one choice was 73.5 and another choice was "cannot be determined from the information given," wouldn't the latter answer be correct because of the missing data re baking powder?
 
bbarmann said:
Thank you Denis for taking the time to deal with this problem.
I see how you arrive at your answer, including the assumption that processing baking powder and flavorings are combined. But this points up to me how imprecise this question is. Why would one assume that the processing of the baking powder is combined with another step when each of these steps is called out separately in the introduction of the question? What's the point of mentioning the baking powder if you then have to assume it's combined with another step? If this was on a multiple choice test, where one choice was 73.5 and another choice was "cannot be determined from the information given," wouldn't the latter answer be correct because of the missing data re baking powder?
Click to expand...

No idea...depends completely on the fuzzy-brained teacher who wrote
up that mess.

I'd do it the way I showed, making sure to note the assumption; but that's me.

I'd also fire the teacher who made that up :twisted:
Why teachers make up problems to teach solving equations by incorporating
some "story" where 90% of the work is trying to understand what the ****
they wrote is beyond me...


That problem can easily be clearly rewritten, something like:

A job requires 5 steps to be completed, taking 100 hours.

Step 1 requires 1/2 hour.
Step 2 requires 8 times Step 1.
Step 3 requires 4 times Step 2.
Step 4 requires 2 hours plus 1/4 of Step 3

How much time does step 5 require?
 
I'll put my 2 cents into the discussion:

1) I completely agree with the way Dennis worked the problem out.

2) My guess is that this problem came out of a textbook, so I'd be careful about castigating a teacher for writing it (though I suppose it is possible that the problem was, in fact, teacher-generated.)

3) Problems which involve math in real life are often not straightforward; one must "sift through" the information to determine which details are pertinent, and how facts relate to each other. I think MAYBE that's one reason the problem was written the way it was....
 
Hmmm....2 more points, then I'm outta here! :

ALL problems given to a student are FROM a teacher, whether the teacher made it up or not: if poorly worded, teacher should know enough to discard it.

ALL problems on a timed test that take time interpreting are UNFAIR.
 
Denis said:
Hmmm....2 more points, then I'm outta here! :

ALL problems given to a student are FROM a teacher, whether the teacher made it up or not: if poorly worded, teacher should know enough to discard it.

ALL problems on a timed test that take time interpreting are UNFAIR.
Click to expand...

Not sure about that last one, Denis.....being able to sort out the important facts in a problem, and solve the problem in a given amount of time MAY be a valid way to interpret a student's ability....
 
Mrspi said:
Not sure about that last one, Denis.....being able to sort out the important facts in a problem, and solve the problem in a given amount of time MAY be a valid way to interpret a student's ability....
Click to expand...
Expecting the student to be able to sort out the facts is one thing. Requiring the student to guess as to what your meaning was before he can even start to do the sorting is, I think, quite another.

The former is asking the student to draw reasonable logical connections and conclusions; the latter is requiring that he read your mind, or just make a wild-arse guess as to what you might have meant -- which seems, to me, less than completely reasonable, especially when this telepathy is being graded.

Just my opinion; I could be wrong....

Eliz.
 
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