Quadratic word problem

316matrix

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May 15, 2019
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The problem: The biology club went on a trip that cost $420 paid equally by each member. At the last minute 6 more students joined. This reduced the cost by $3 per student. How many students went on the trip?

I set it up like this..
original cost per person is c = 420/n
new cost per person is c-3 = 420/(n+6)

I simplified the new cost equation to say (c-3)(n+6)=420

I then substituted "c" with 420/n like this

(420/n-3)(n+6)=420

I solved and got 26.13 students. How can 0.13 students go on the trip? I must have done something wrong.
 

Dr.Peterson

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I get the same answer by a very different method. Check whether you copied the problem wrong!
 

Otis

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... At the last minute 6 more students joined ...

I solved and got 26.13 students ... I must have done something wrong.
Hello. Maybe your materials contain a typo. The answer is a Whole number, if we change "6 more students" to "7 more students".

By the way, when you solved for n, you forgot to add 6 to it. So, if you try again using (n+7), don't forget to add 7 to your solution for n.

😎
 

316matrix

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Thank you both. The problem is exactly the same as the worksheet. I didn't add the 6 back in because I thought it would still render me a 0.13 in my answer.

Thanks a ton!
 

Dr.Peterson

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The point about adding 6 is that you are asked how many actually went on the trip, while your n is the number that originally planned to go. So 26.13 would not answer the question. But like you, I stopped when I found n was not an integer, and didn't continue to answer the question.

Have you tried it with 7 in place of the 6? What answer do you get (for the question asked)?

Let us know when your teacher says what the problem was supposed to say!
 

316matrix

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I will definitely let the teacher know that 7 seems to work as 6 does not.
With 7 I get n= 28. Which adds to "7 more students" (in the new case) to get 35.
 
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