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The cost of chartering a plane was shared equally among 30 passengers.

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Bunuel
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The cost of chartering a plane was shared equally among 30 passengers. [#permalink] The cost of chartering a plane was shared equally among 30 passengers.   22 May 2020, 09:55
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94% (01:56) correct 6% (02:06) wrong based on 155 sessions
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The cost of chartering a plane was shared equally among 30 passengers. If there had been 35 passengers sharing that cost, the cost per passenger would have been $30 less. What was the cost of chartering the plane?

A. $5,400
B. $6,125
C. $6,300
D. $6,800
E. $7,350

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C
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Re: The cost of chartering a plane was shared equally among 30 passengers. [#permalink] The cost of chartering a plane was shared equally among 30 passengers.   22 May 2020, 10:04
Answer is C

Let the cost of chartering the plane is X
The per passenger cost be y

When there are 30 passengers chartering the plane cost pee head is.
X/30=Y => X=30Y ---------(1)

If there were 35 passengers, the cost per head would have lessen by 30$.
X/35=(Y-30) => X=35Y-1050 -----(2)

Equating both equations,
30Y = 35Y-1050
5Y=1050
Y=210

The cost of chartering the plane is 30*y => 30*210 => 6300$

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Re: The cost of chartering a plane was shared equally among 30 passengers. [#permalink] The cost of chartering a plane was shared equally among 30 passengers.   22 May 2020, 10:06
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Bunuel wrote:
The cost of chartering a plane was shared equally among 30 passengers. If there had been 35 passengers sharing that cost, the cost per passenger would have been $30 less. What was the cost of chartering the plane?

A. $5,400
B. $6,125
C. $6,300
D. $6,800
E. $7,350

PS20354


from given info we know
x/35 = x/30 - 30
solve for x = $ 6300
OPTION C
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Re: The cost of chartering a plane was shared equally among 30 passengers. [#permalink] The cost of chartering a plane was shared equally among 30 passengers.   24 May 2020, 03:28
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C.

Let total Price be x.

Price per passenger when shared by 30 passengers = x/30
Price per passenger when shared by 35 passengers = x/35

As per qtn: x/30 - x/35 = 30

Solving for x: x = 6800
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The cost of chartering a plane was shared equally among 30 passengers. [#permalink] The cost of chartering a plane was shared equally among 30 passengers.   26 Nov 2020, 19:48
Bunuel wrote:
The cost of chartering a plane was shared equally among 30 passengers. If there had been 35 passengers sharing that cost, the cost per passenger would have been $30 less. What was the cost of chartering the plane?

A. $5,400
B. $6,125
C. $6,300
D. $6,800
E. $7,350

PS20354


Cost of plane = \(C\)
Cost shared equally among 30 passengers: \(\frac{C}{30}\)
Cost shared equally among 35 passengers: \(\frac{C}{35}\)

\(\frac{C}{35} = \frac{C}{30} -1\)

\(\frac{C}{35} = \frac{C}{30} - \frac{30}{30}\)

\(\frac{C}{35} = \frac{C-30}{30}\)

\(C = 210\)

\(210 * 30 = $6,300\)
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Re: The cost of chartering a plane was shared equally among 30 passengers. [#permalink] The cost of chartering a plane was shared equally among 30 passengers.   28 Nov 2020, 01:21
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Solution



Given
In this question, we are given that
    • The cost of chartering a plane was shared equally among 30 passengers
    • If there had been 35 passengers sharing that cost, the cost per passenger would have been $30 less

To find
We need to determine
    • The cost of chartering the plane

Approach and Working out
Apart from the already mentioned equation-solving approach, we can get the answer using the options also.
    • As the cost can be equally divided by either among 30 passengers or among 35 passengers, we can say the total cost is a multiple of both 30 or 35, or a multiple of LCM (30, 35) = 210
Among the given options, only 6300 and 7350 are divisible by 210

If we check 6300 first,
    • 6300 = 30 x 210 = 35 x 180 (difference in cost is 210 – 180 = 30)

Thus, option C is the correct answer.

Correct Answer: Option C
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Re: The cost of chartering a plane was shared equally among 30 passengers. [#permalink] The cost of chartering a plane was shared equally among 30 passengers.   20 May 2024, 06:43
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­The total costs are equal in either scenario. Set them equal in terms of x dollars per person:

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Re: The cost of chartering a plane was shared equally among 30 passengers. [#permalink]
20 May 2024, 06:43
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