SOLUTION: a group of students decided to purchase a tv ranging from 170 to 195 $. but at the last moment, two students backed out of the decision so that the remaining students had to pay 10

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Question 598841: a group of students decided to purchase a tv ranging from 170 to 195 $. but at the last moment, two students backed out of the decision so that the remaining students had to pay 10 $. more than they had planned. find the cost of the tv if the amount has been shared equally among the students.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a group of students decided to purchase a tv ranging from 170 to 195 $.
but at the last moment, two students backed out of the decision so that the remaining students had to pay 10 $. more than they had planned.
find the cost of the tv if the amount has been shared equally among the students.
:
Let c = cost of the TV
Let s = original number of students
then
(s-2) = actual number of students that paid
:
c%2F%28%28s-2%29%29 - c%2Fs = 10
multiply by s(s-2), clear the denominators, results:
cs - c(s-2) = 10s(s-2)
cs - cs + 2c = 10s^2 - 20s
2c = 10s^2 - 20s
divide eq by 2
c = 5s^2 - 10s
We know that c has to be between 170 and 195
A little substitution for s reveals that only value for c is $175, when s=7 (original number students)
:
Check this actual number students are 5
175/5 = $35
175/7 = $25