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The cost of a certain school trip was $16 for each child and $24 for

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Bunuel
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The cost of a certain school trip was $16 for each child and $24 for [#permalink] New post   02 Aug 2023, 05:00
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The cost of a certain school trip was $16 for each child and $24 for each adult. What was the ratio of the number of children to the number of adults on the trip?

(1) The ratio of the total cost of the trip for all children to the total cost of the trip for all adults was 8 to 3.
(2) The total cost of the trip for all children and adults together was $2,200.
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Re: The cost of a certain school trip was $16 for each child and $24 for [#permalink] New post   02 Aug 2023, 23:02
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Bunuel wrote:
The cost of a certain school trip was $16 for each child and $24 for each adult. What was the ratio of the number of children to the number of adults on the trip?

(1) The ratio of the total cost of the trip for all children to the total cost of the trip for all adults was 8 to 3.
(2) The total cost of the trip for all children and adults together was $2,200.


  • Number of adults = \(a\)
  • Number of children = \(c\)

Question : \(\frac{c}{a}\)

Statement 1

(1) The ratio of the total cost of the trip for all children to the total cost of the trip for all adults was 8 to 3.

\(\frac{16c }{ 24a} = \frac{8}{3}\)

We can find the ratio of \(\frac{c}{a}\).

Hence, this statement is sufficient. We can eliminate B, C, and E.

Statement 2

(2) The total cost of the trip for all children and adults together was $2,200

\(16c + 24a = 2200\)

\(2c + 3a = 275\)

We can have multiple values of c and a satisfying the equation.

\(c = 22, a = 77\) ; \(\frac{c }{ a} = \frac{2}{7}\)

\(c = 46, a = 71\) ; \(\frac{c }{ a} = \frac{46}{71}\)

The statement alone is not sufficient.

Option A
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Re: The cost of a certain school trip was $16 for each child and $24 for [#permalink] New post   06 Sep 2023, 18:20
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Bunuel wrote:
The cost of a certain school trip was $16 for each child and $24 for each adult. What was the ratio of the number of children to the number of adults on the trip?

(1) The ratio of the total cost of the trip for all children to the total cost of the trip for all adults was 8 to 3.
(2) The total cost of the trip for all children and adults together was $2,200.


The prices were $16 per child and $24 per adult, and we need to answer the question:

# of children (c) : # of adults (a)= ?

Statement One Alone:

=> The ratio of the total cost of the trip for all children to the total cost of the trip for all adults was 8 to 3.

Total cost for children : Total cost for adults = 8 : 3

16c/24a = 8/3
2c/3a = 8/3
c/a = 4/1 => c : a = 4 : 1

Statement one is sufficient. Eliminate answer choices B, C, and E.

Statement Two Alone:

=> The total cost of the trip for all children and adults together was $2,200.

16c + 24a = 2,200
2c + 3a = 275

If there were 100 children and 25 adults, then c : a = 100 : 25 = 4 : 1.

Whereas, if there were 25 children and 75 adults, then c : a = 25 : 75 = 1 : 3.

Statement two is not sufficient.

Answer: A
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Re: The cost of a certain school trip was $16 for each child and $24 for [#permalink] New post   22 Jan 2024, 06:31
I always have trouble during the exam to check such possibilities of different numbers that can satisfy an equation. I end up either picking the wrong combos, getting only 1 pair to work and calling such a statement sufficient OR end up wasting time either way. Any work arounds or suggestions would be very helpful JeffTargetTestPrep !
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Re: The cost of a certain school trip was $16 for each child and $24 for [#permalink]
22 Jan 2024, 06:31
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