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02 Aug 2023, 05:00
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A
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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.
(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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02 Aug 2023, 23:02
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Bunuel
- 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
18 Jul 2024, 00:22
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ellewoods2
We use the concept of integer solutions to equations in 2 variables here. The moment we get one solution, we know all other possible solutions, if there are any.
It has been discussed here:
https://anaprep.com/algebra-integer-sol ... variables/
Given equation: 2c+3a=275
We can see straightaway that a = 1 will satisfy because 275 - 3 = 272 (an even number) so we will get 2c = 272 which will give us c = 136 Hence a = 1, c = 136 is a possible solution.
Next possible solution is a = 3, c = 133
Next possible solution is a = 5, c = 130
and so on...
(The logic has been discussed in the blog post given above)
