SOLUTION: A math class planned a field trip to a computer center. The trip cost $240 to be paid equally by each student. 4 students suddenly can't go. This increased the cost by $2 per stude

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Question 143386This question is from textbook algebra: structure and method: book1
: A math class planned a field trip to a computer center. The trip cost $240 to be paid equally by each student. 4 students suddenly can't go. This increased the cost by $2 per student. How many students went to the computer center? HELP MUCH APPRECIATED!!!! This question is from textbook algebra: structure and method: book1

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let n=# of total students and c=cost per student (assuming they all go)



So if everyone goes, then the total cost $240 is divided equally among all n students. So the individual cost is

c=240%2Fn



However, if 4 don't go, then simply subtract 4 from n to get n-4. Now divide 240 by n-4 to get the individual cost plus $2


240%2F%28n-4%29=c%2B2



240%2F%28n-4%29=240%2Fn%2B2 Plug in c=240%2Fn


n%2Across%28%28n-4%29%29%28240%2Fcross%28n-4%29%29=n%28n-4%29%28240%2Fcross%28n%29%2B2%29 Multiply both sides by the LCD n%28n-4%29. This will clear the fractions


240n=240%28n-4%29%2B2n%28n-4%29 Distribute


240n=240n-960%2B2n%5E2-8n Distribute again


0=240n-960%2B2n%5E2-8n-240n Subtract 240n from both sides.


0=2n%5E2-8n-960 Combine like terms




0=2%28n-24%29%28n%2B20%29 Factor the right side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
n-24=0 or n%2B20=0

n=24 or n=-20 Now solve for n in each case


So our possible answers are

n=24 or n=-20



However, since a negative number of students doesn't make any sense, this means that our only answer is n=24



So there are a total of 24 students. Since 4 can't go, there are only 20 students who went to the computer center.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A math class planned a field trip to a computer center. The trip cost $240 to be paid equally by each student. 4 students suddenly can't go. This increased the cost by $2 per student. How many students went to the computer center?
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Let original number in class be "x"
Total cost for the group was 240x dollars
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Average cost when 4 cannot go : 240x/(x-4)
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EQUATION:
new average - old average = 2 dollars
240x/(x-4) - 240 = 2
240x/(x-4) = 242
240x = 242x - 968
2x = 968
x = 484 (# of students who planned to go to the computer center)
x-4 = 480 (# of students who actually went)
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Cheers,
Stan H.