A group of friends charters a boat for $540, and each person contribut

Question

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

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

GMATWhizTeam · Accepted Answer

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.

Kinshook · Answer

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

Archit3110 · Answer

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

Archit3110 · Answer

Kinshook 
please see highlighted part shouldnt it be n+3 ; as we are adding 3 more people.....

Kinshook · Answer

HI  Archit3110

I have assumed x to be total number of people including 3 added ones. That creates the difference in equation.

ScottTargetTestPrep · Answer

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

johnnymbikes · Answer

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)

bumpbot · Answer

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A group of friends charters a boat for $540, and each person contribut

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