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I find this wording sloppily ambiguous: "The food truck's revenue from selling a total of 209 salads and drinks in one day was $836.50." On initial read, I tho

I find this wording sloppily ambiguous: "The food truck's revenue from selling a total of 209 salads and drinks in one day was $836.50." On initial read, I thought it was saying 209 salads and 209 drinks. Now, obviously the question would be trivial and the total revenue impossible it that were the case, but I wish in general that math questions were written much less ambiguously.

jchendy 11y ago
I noticed the same. It could easily be fixed by specifying "...revenue from selling a combined total of..."
- jsprogrammer 11y ago
  'Total' already implies 'combined'.
  - thrownaway2424 11y ago
    Yes, but the sentence could be parsed (and was initially parsed by me) as 209 salads and an unknown number of drinks.
    - jsprogrammer 11y ago
      Without a comma, I believe, 'salads and drinks' must be parsed as belonging together and are modified by the most recently occurring number (209).
chasing 11y ago
I mean, part of applying logic to the problem is saying, "Well, clearly they don't mean 209 salads and 209 drinks, since that's $1776.50 and they say right there that the take was $836.50." I'm okay with that sort of logical reading comprehension being part of the test. It certainly feels like an important real-world skill...
- rrauenza 11y ago
  I think it's just sloppy and unintentional, especially for a timed test. I find things like this common in my kids' Math homework. (I don't blame common core, I blame bad text book writers.) I also had to run the interpretation of 209 "salads and an unknown number of drinks" through my head as I parsed it. I do see the value in learning how to remove ambiguity when trying to solve a problem, but I'm not convinced that is what they are intentionally testing. On the other hand, I really liked how it says you may not use a calculator on the ones that did not need a calculator -- especially when running off to a calculator would have only made things worse!
fragsworth 11y ago
While it might be frustrating, this kind of question is entirely appropriate. Even though there is an ambiguity in small component of the question, when you take it in the context of the rest of the question, the ambiguity is removed. As a result, it tests your ability to reason about the intent of the author.
untog 11y ago
I wish in general that math questions were written much less ambiguously. There's an argument to be made that real life is never that way, so we should be preparing students to evaluate ambiguities in questions.
- delinka 11y ago
  And preparing them for the inevitability that ambiguities will be misinterpreted by others including themselves. To that end, this question should have no correct answer.
socalnate1 11y ago
I totally agree, I assumed the question had an error in it and spent my time trying to figure out what the error was.
pc86 11y ago
I don't know that I've ever read a statement where something like "209 salads and drinks" meant 209 of each and not 209 total.
- bas 11y ago
  For instance, "100 boys and girls in the class". I read that as 100 students total, not 100 of each.
  - rrauenza 11y ago
    I think the difference is context. You would normally expect a drink with each salad.
- lettercarrier 11y ago
  If "209 drinks and salads" were on the evenings sheet for a wedding, it would mean 209 of each. Furthermore, if a worker would come up to me an question, "Does this mean 209 of each" I would think he kid is not bright and needs direction for everything????!!!!
anon4 11y ago
I'm more perplexed by how to solve it, since any odd number of salads is a solution. I.e. for every k, 836.5 - 6.5 * (2 * k + 1) is an even number
- dastbe 11y ago
  I'm not quite sure where you're going with k vs k+1. we know that s + d = 209 (1) and we know that 6.5s + 2d = 836.5 (2) we can rewrite (1) as d = 209 - s (3) substituting (3) into (2) we get 6.5s + 2(209 - s) = 836.5 (4) solving (4) for s yields s = 93 (5) alternatively, you can solve the system of linear equations [ 1 1 ] [ s ] = [ 209 ] [ 6.5 2 ] [ d ] = [ 836.5 ] (1) [ s ] = [ -4/9 2/9 ] [ 209 ] [ d ] = [ 13/9 -2/9 ] [ 836.5 ] (2) [ s ] = [ 93 ] [ d ] = [ 116 ] (3)
  - castratikron 11y ago
    That's how I did it. rref() on a TI83 is extremely useful.
- rtkwe 11y ago
  It's a really standard form of 2 formula substitution, you're missing the fact that there was 209 drinks and salads sold combined which constrains the solution to a single answer. From the setup you get 2 equations where x is the number of salads and y is the number of drinks: > [1] 6.5x + 2 y = 836.5 and > [2] x + y = 209 Solve [2] for y and substitute into [1]: > 6.5*x + 2(209 - x) = 836.5 You can also do this with linear algebra but this is the way I would have known as a normal high schooler taking the SAT.

jchendy 11y ago

I noticed the same. It could easily be fixed by specifying "...revenue from selling a combined total of..."

jsprogrammer 11y ago
'Total' already implies 'combined'.
- thrownaway2424 11y ago
  Yes, but the sentence could be parsed (and was initially parsed by me) as 209 salads and an unknown number of drinks.
  - jsprogrammer 11y ago
    Without a comma, I believe, 'salads and drinks' must be parsed as belonging together and are modified by the most recently occurring number (209).

chasing 11y ago

I mean, part of applying logic to the problem is saying, "Well, clearly they don't mean 209 salads and 209 drinks, since that's $1776.50 and they say right there that the take was $836.50." I'm okay with that sort of logical reading comprehension being part of the test. It certainly feels like an important real-world skill...

rrauenza 11y ago
I think it's just sloppy and unintentional, especially for a timed test. I find things like this common in my kids' Math homework. (I don't blame common core, I blame bad text book writers.) I also had to run the interpretation of 209 "salads and an unknown number of drinks" through my head as I parsed it. I do see the value in learning how to remove ambiguity when trying to solve a problem, but I'm not convinced that is what they are intentionally testing. On the other hand, I really liked how it says you may not use a calculator on the ones that did not need a calculator -- especially when running off to a calculator would have only made things worse!

fragsworth 11y ago

While it might be frustrating, this kind of question is entirely appropriate. Even though there is an ambiguity in small component of the question, when you take it in the context of the rest of the question, the ambiguity is removed. As a result, it tests your ability to reason about the intent of the author.

untog 11y ago

I wish in general that math questions were written much less ambiguously. There's an argument to be made that real life is never that way, so we should be preparing students to evaluate ambiguities in questions.

delinka 11y ago
And preparing them for the inevitability that ambiguities will be misinterpreted by others including themselves. To that end, this question should have no correct answer.

socalnate1 11y ago

I totally agree, I assumed the question had an error in it and spent my time trying to figure out what the error was.

pc86 11y ago

I don't know that I've ever read a statement where something like "209 salads and drinks" meant 209 of each and not 209 total.

bas 11y ago
For instance, "100 boys and girls in the class". I read that as 100 students total, not 100 of each.
- rrauenza 11y ago
  I think the difference is context. You would normally expect a drink with each salad.
lettercarrier 11y ago
If "209 drinks and salads" were on the evenings sheet for a wedding, it would mean 209 of each. Furthermore, if a worker would come up to me an question, "Does this mean 209 of each" I would think he kid is not bright and needs direction for everything????!!!!

anon4 11y ago

I'm more perplexed by how to solve it, since any odd number of salads is a solution. I.e. for every k, 836.5 - 6.5 * (2 * k + 1) is an even number

dastbe 11y ago
I'm not quite sure where you're going with k vs k+1. we know that s + d = 209 (1) and we know that 6.5s + 2d = 836.5 (2) we can rewrite (1) as d = 209 - s (3) substituting (3) into (2) we get 6.5s + 2(209 - s) = 836.5 (4) solving (4) for s yields s = 93 (5) alternatively, you can solve the system of linear equations [ 1 1 ] [ s ] = [ 209 ] [ 6.5 2 ] [ d ] = [ 836.5 ] (1) [ s ] = [ -4/9 2/9 ] [ 209 ] [ d ] = [ 13/9 -2/9 ] [ 836.5 ] (2) [ s ] = [ 93 ] [ d ] = [ 116 ] (3)
- castratikron 11y ago
  That's how I did it. rref() on a TI83 is extremely useful.
rtkwe 11y ago
It's a really standard form of 2 formula substitution, you're missing the fact that there was 209 drinks and salads sold combined which constrains the solution to a single answer. From the setup you get 2 equations where x is the number of salads and y is the number of drinks: > [1] 6.5x + 2 y = 836.5 and > [2] x + y = 209 Solve [2] for y and substitute into [1]: > 6.5*x + 2(209 - x) = 836.5 You can also do this with linear algebra but this is the way I would have known as a normal high schooler taking the SAT.