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An institute charges $ for one time registration and $ per session for
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19 Apr 2023, 08:10
19 Apr 2023, 08:10
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83% (01:55) correct
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An institute charges $ n/2 for one time registration and $ 3n/2 per session for first ‘n’ sessions after which each session is charged $n only. If a student paid $60 for (n + 4) sessions he attended, including the registration fee, what is the value of n?
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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
Re: An institute charges $ for one time registration and $ per session for
[#permalink]
19 Apr 2023, 19:47
19 Apr 2023, 19:47
1
Expert Reply
The registration fee is n/2.
For the first n sessions, the cost per session is $3n/2.
So the total cost for the first n sessions is (n sessions) x ($3n/2 per session) = $3n^2/2.
After the first n sessions, the cost per session is n.
So the total cost for the (n + 4) sessions is:
(n/2) + ($3n^2/2) + [(n + 4 - n) x n]
Simplifying this expression:
(n/2) + ($3n^2/2) + (4 x n)
= (n/2) + (4n) + ($3n^2/2)
= $3n^2/2 + (9n/2)
We know that this total cost is equal to $60:
$3n^2/2 + (9n/2) = $60
Multiplying both sides by 2/3:
$n^2 + 3n = $40
Rearranging the terms:
$n^2 + 3n - $40 = 0
Factoring the left side of the equation:
(n + 8)(n - 5) = 0
Therefore, n = -8 or n = 5.
We can ignore the negative solution because n must be a positive integer.
Therefore, the value of n is 5.
Hence, the answer is 5.
For the first n sessions, the cost per session is $3n/2.
So the total cost for the first n sessions is (n sessions) x ($3n/2 per session) = $3n^2/2.
After the first n sessions, the cost per session is n.
So the total cost for the (n + 4) sessions is:
(n/2) + ($3n^2/2) + [(n + 4 - n) x n]
Simplifying this expression:
(n/2) + ($3n^2/2) + (4 x n)
= (n/2) + (4n) + ($3n^2/2)
= $3n^2/2 + (9n/2)
We know that this total cost is equal to $60:
$3n^2/2 + (9n/2) = $60
Multiplying both sides by 2/3:
$n^2 + 3n = $40
Rearranging the terms:
$n^2 + 3n - $40 = 0
Factoring the left side of the equation:
(n + 8)(n - 5) = 0
Therefore, n = -8 or n = 5.
We can ignore the negative solution because n must be a positive integer.
Therefore, the value of n is 5.
Hence, the answer is 5.
gmatclubot
Re: An institute charges $ for one time registration and $ per session for [#permalink]
19 Apr 2023, 19:47
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