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Jima Posted 11 years ago
Grammar
Interpreting SAT I math question
ok... I know that this is not a math forum, but I am asking this question because I have trouble understanding the problem itself.
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In a certain high school, there are three times as many band members as orchestra members and twice as many orchestra members as jazz choir members. If no students can be enrolled in more than one of the three activities and there are 108 members in the three activities, how many students are in the band?
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I especially have hard time interpreting "there are three times as many band members as orchestra members and twice as many orchestra members as jazz choir members." My teacher says that we should set up equation as:
Band = 3 Orchestra
Orchestra = 2 Jazz
Band + Orchestra + Jazz = 108
However, more I read this problem, I come up with this equation:
3 Band = Orchestra
2 Orchestra = Jazz
Band + Orchestra + Jazz = 108
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Of course, my equation is a complete reversal of my teacher's equation. This discrepancy indicates that one of us did something wrong setting up the equation. I do know that this is not a math forum, but since I believe that this difference comes from our (or maybe my) understanding of English, I decided to post this question in English forum. And I am aware that there are easier way to approach this problem (e.g. setting up ratios, etc.), but I would like to see how we can solve this problem by using systems of equations. Thank you!
P.S The answer is 72 band members.
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In a certain high school, there are three times as many band members as orchestra members and twice as many orchestra members as jazz choir members. If no students can be enrolled in more than one of the three activities and there are 108 members in the three activities, how many students are in the band?
--
I especially have hard time interpreting "there are three times as many band members as orchestra members and twice as many orchestra members as jazz choir members." My teacher says that we should set up equation as:
Band = 3 Orchestra
Orchestra = 2 Jazz
Band + Orchestra + Jazz = 108
However, more I read this problem, I come up with this equation:
3 Band = Orchestra
2 Orchestra = Jazz
Band + Orchestra + Jazz = 108
--
Of course, my equation is a complete reversal of my teacher's equation. This discrepancy indicates that one of us did something wrong setting up the equation. I do know that this is not a math forum, but since I believe that this difference comes from our (or maybe my) understanding of English, I decided to post this question in English forum. And I am aware that there are easier way to approach this problem (e.g. setting up ratios, etc.), but I would like to see how we can solve this problem by using systems of equations. Thank you!
P.S The answer is 72 band members.
Top answer
I agree with your teacher here . I am no good at algebra, so here's how I would solve this: We have 1 "jazz group"; let's call the number in the group n . We have 1 "orchestra group", which is twice the size of the "jazz group", so there are 2n members of the orchestra.
- I agree with your teacher here .
- I am no good at algebra, so here's how I would solve this: We have 1 "jazz group"; let's call the number in the group n .
- We have 1 "orchestra group", which is twice the size of the "jazz group", so there are 2n members of the orchestra.
- We have 1 "band group", which is three times the size of the "orchestra group", so there are 3x 2n members of the band = 6n .
- We know that jazz + orchestra + band = 108.
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1 Answers
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I agree with your teacher here 
.
I am no good at algebra, so here's how I would solve this:
We have 1 "jazz group"; let's
.I am no good at algebra, so here's how I would solve this:
We have 1 "jazz group"; let's
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