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A club offers discounted membership for $2x each for the first two peo
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17 Apr 2023, 01:42
17 Apr 2023, 01:42
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7% (02:01) correct
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A club offers discounted membership for $2x each for the first two people and charged $(x + n) for each member who joins thereafter. 5 friends, Alice, Beth, Clain, Dino and Eric were the first to join the club, paid a total of $75 as the fee. If x and n are positive integers and n + x < 20, what could be the value of n?
Indicate all that apply
4
11
15
18
25
Indicate all that apply
4
11
15
18
25
Re: A club offers discounted membership for $2x each for the first two peo
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26 May 2023, 22:29
26 May 2023, 22:29
Expert Reply
OE
It is given that a club offers discounted membership for $2๐ฅ each for the first two
people and charged $(๐ฅ + ๐) for each member who joins thereafter. 5 friends, A, B,
C, D and E were the first to join the club, paid a total of $75 as the fee. ๐ฅ and ๐ are
positive integers and ๐ + ๐ฅ < 20, we need to find the possible values of ๐.
The charges for the first two member = 2 ร 2๐ฅ = 4๐ฅ
The charges for the remaining 3 members = 3(๐ฅ + ๐) = 3๐ฅ + 3๐
According to the question,
4๐ฅ + 3๐ฅ + 3๐ = 75
i.e. 7๐ฅ + 3๐ = 75
n=75-7x/3
n=25-7x/3 (equation 1)
Now, ๐ฅ must be a multiple of 3, to the given integer value of n.
Hence, ๐ฅ can be 3, 6, 9. (๐ฅ canโt be more than 9 as n will become negative).
Therefore, when, ๐ฅ = 3; ๐ = 25 โ7*3/3=18
x=6 and n=25-7*6/3=11
x=9 and n=25-7*9/3=4
A, B, and D are the correct options
It is given that a club offers discounted membership for $2๐ฅ each for the first two
people and charged $(๐ฅ + ๐) for each member who joins thereafter. 5 friends, A, B,
C, D and E were the first to join the club, paid a total of $75 as the fee. ๐ฅ and ๐ are
positive integers and ๐ + ๐ฅ < 20, we need to find the possible values of ๐.
The charges for the first two member = 2 ร 2๐ฅ = 4๐ฅ
The charges for the remaining 3 members = 3(๐ฅ + ๐) = 3๐ฅ + 3๐
According to the question,
4๐ฅ + 3๐ฅ + 3๐ = 75
i.e. 7๐ฅ + 3๐ = 75
n=75-7x/3
n=25-7x/3 (equation 1)
Now, ๐ฅ must be a multiple of 3, to the given integer value of n.
Hence, ๐ฅ can be 3, 6, 9. (๐ฅ canโt be more than 9 as n will become negative).
Therefore, when, ๐ฅ = 3; ๐ = 25 โ7*3/3=18
x=6 and n=25-7*6/3=11
x=9 and n=25-7*9/3=4
A, B, and D are the correct options
Re: A club offers discounted membership for $2x each for the first two peo
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06 Sep 2023, 11:42
06 Sep 2023, 11:42
2
If n is 18, then x is 3 and the sum of these two number will be 21, which is impossible since n + x < 20. I think the answer should be A and B. Please let me know what you think.
