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Bunuel
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A group of friends charters a boat for $540, and each person contribut 17 Mar 2020, 08:48
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C
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45% (medium)

Question Stats:

75% (02:58) correct 25% (03:11) wrong based on 402 sessions

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A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less. If they find three more friends to join them, what is the total number of people renting the boat?

(A) 6
(B) 9
(C) 15
(D) 18
(E) 21
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C
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A group of friends charters a boat for $540, and each person contribut 17 Mar 2020, 23:23
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Bunuel
A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less. If they find three more friends to join them, what is the total number of people renting the boat?

(A) 6
(B) 9
(C) 15
(D) 18
(E) 21

Solution


    • Let us assume that the initially there were x number of friends in the group.
      o After 3 more friends joined the group, the total number of people becomes \(x+3\).
We need to find the value of \(x+3\).
    • Now, \(\frac{540}{x} – \frac{540}{x+3} = 9 \)
      \(⟹ 540 (\frac{1}{x} – \frac{1}{x+3}) = 9\)
      \(⟹ 540 *\frac{3}{(x)(x+3)} = 9\)
      \(⟹ \frac{180}{(x)(x+3)} = 1\)
    • Since we know that x and x+3 must be integers, we can write above equation as,
      o \(\frac{180}{(x)(x+3)} = 1 = \frac{180}{12*15}\)
      o On comparing both the sides we get, \(x = 12\) and \(x+3 = 15\)
Thus, the correct answer is Option C.
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A group of friends charters a boat for $540, and each person contribut Updated on: 17 Mar 2020, 10:23
Originally posted by Kinshook on 17 Mar 2020, 10:11.
Last edited by Kinshook on 17 Mar 2020, 10:23, edited 1 time in total.
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Bunuel
A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less. If they find three more friends to join them, what is the total number of people renting the boat?

(A) 6
(B) 9
(C) 15
(D) 18
(E) 21

Given: A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less.

Asked: If they find three more friends to join them, what is the total number of people renting the boat?

Let the total number of people renting the boat be x

540 / (x-3) - 540/x=9

For x=15
45 - 36 = 9

IMO C
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A group of friends charters a boat for $540, and each person contribut 17 Mar 2020, 10:16
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Bunuel
A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less. If they find three more friends to join them, what is the total number of people renting the boat?

(A) 6
(B) 9
(C) 15
(D) 18
(E) 21

let initial total people be n

so avg costing ; 540/n
after 3 more people join we get
540/n+3 = 540/n-9
solve for n
9n^2+27n-1620=0
n^2+3n-180=0
n=-15,+12
cannot be -ve
so n=12 ; and after 3 more people join total becomes 15
IMO C ; 15
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A group of friends charters a boat for $540, and each person contribut 17 Mar 2020, 10:18
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Kinshook
please see highlighted part shouldnt it be n+3 ; as we are adding 3 more people.....


Kinshook
Bunuel
A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less. If they find three more friends to join them, what is the total number of people renting the boat?

(A) 6
(B) 9
(C) 15
(D) 18
(E) 21

Given: A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less.

Asked: If they find three more friends to join them, what is the total number of people renting the boat?

Let the total number of people renting the boat be x

540 / (x-3) - 540/x=9

x=15
45 - 36 = 9

IMO C
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A group of friends charters a boat for $540, and each person contribut 17 Mar 2020, 10:22
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Kinshook
please see highlighted part shouldnt it be n+3 ; as we are adding 3 more people.....


Kinshook
Bunuel
A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less. If they find three more friends to join them, what is the total number of people renting the boat?

(A) 6
(B) 9
(C) 15
(D) 18
(E) 21

Given: A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less.

Asked: If they find three more friends to join them, what is the total number of people renting the boat?

Let the total number of people renting the boat be x

540 / (x-3) - 540/x=9

x=15
45 - 36 = 9

IMO C

HI Archit3110

I have assumed x to be total number of people including 3 added ones. That creates the difference in equation.
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A group of friends charters a boat for $540, and each person contribut 18 Apr 2023, 17:59
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Bunuel
A group of friends charters a boat for $540, and each person contributes equally to the cost. They determine that if they can get three more of their friends to join them, every person in the group will pay $9 less. If they find three more friends to join them, what is the total number of people renting the boat?

(A) 6
(B) 9
(C) 15
(D) 18
(E) 21

We can let the number of friends = n, then create the equation:

540/n - 9 = 540/(n+3)

Mulifplying by n(n+3), we have:

540(n+3) - 9n(n+3) = 540n

540n + 1,620 - 9n^2 - 27n = 540n

9n^2 + 27n - 1,620 = 0

n^2 + 3n - 180 = 0

(n + 15)(n - 12) = 0

n = 12, so when three more friends join, there are 15 friends.

Answer: C
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A group of friends charters a boat for $540, and each person contribut 07 Aug 2023, 22:56
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A more intuitive approach:

Let P = price paid, Q = # of friends
(1) P * Q = 540
(2) (P-9)*(Q+3) =540
PQ + 3P - 9Q - 27 = 540 (sub in PQ = 540 from (1))
540 + 3P - 9Q - 27 = 540 (540's cancel out)
3P - 9Q - 27 = 0
P - 3Q - 9 = 0
P - 3Q = 9
540/Q - 3Q = 9 (common denominator of Q)

(540 - 3Q^2)/Q = 9
3Q^2 + 9Q - 540 = 0
Q^2 + 3Q - 180 = 0

Factor: (Q + 18) ( Q - 15) = 0
.'. Q = 15 or Q = -18

can't be a negative number so Q = 15 (C)
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A group of friends charters a boat for $540, and each person contribut 11 Jul 2025, 09:42
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