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The ratio of spinsters to cats is 2 to 7. If there are 25

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The ratio of spinsters to cats is 2 to 7. If there are 25  [#permalink]

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New post 01 Jun 2012, 10:19
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The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?

A. 10
B. 12
C. 15
D. 18
E. 27
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Posts: 118
Re: Ratio Problem 4  [#permalink]

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New post 01 Jun 2012, 22:18
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phoenix9801 wrote:
The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks


The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?
A) 10
B) 12
C) 15
D) 18
E) 27


Hi phoenix9801,

In these questions, you can easily notice that there are 2 variables: spinsters and cats and two facts provided. So it is a case of 2 equations in 2 variables.

Let no of spinsters and cats be S and C respectively.
Equation 1:
S/C = 2/7
=> 7S = 2C

Equation 2:
C = S + 25

Insert this in equation 1 => 7S = 2 (S + 25)
=> 7S = 2S + 50
=> 5S = 50
=> S = 10

Hence the answer is (A)

Hope that helps.
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Re: Ratio Problem 4  [#permalink]

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New post 02 Jun 2012, 01:29
1
phoenix9801 wrote:
The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks


The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?
A) 10
B) 12
C) 15
D) 18
E) 27


Let the common multiplier for ratio be x
Such that Cats = 7x and Spinsters be 2x
cats-spins = 7x - 2x = 5x

but cats are 25 more than spinsters

5x=25; x=5

Spinsters = 2x = 2*5 = 10

A is my choice
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Re: The ratio of spinsters to cats is 2 to 7. If there are 25  [#permalink]

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New post 02 Jun 2012, 05:59
2
phoenix9801 wrote:
The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks

The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?

A. 10
B. 12
C. 15
D. 18
E. 27


Given: \(\frac{spinsters}{cats}=\frac{2x}{7x}\) for some positive integer multiple \(x\). Also given that \(7x-2x=25\) --> \(x=5\) --> \(spinsters=2x=10\).

Answer: A.
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Re: The ratio of spinsters to cats is 2 to 7. If there are 25  [#permalink]

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New post 29 Dec 2017, 12:44
Top Contributor
phoenix9801 wrote:
The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?

A. 10
B. 12
C. 15
D. 18
E. 27


Another option is to list equivalent ratios

GIVEN: The ratio of spinsters to cats is 2 to 7
So, it's possible that there are 2 spinsters and 7 cats [difference = 7 - 2 = 5.....we need a difference of 5]
It's also possible that there are 4 spinsters and 14 cats [difference = 14 - 4 = 10.....we need a difference of 5]
Or there are 6 spinsters and 21 cats [difference = 15.....we need a difference of 5]
Or there are 8 spinsters and 28 cats [difference = 20.....we need a difference of 5]
Or there are 10 spinsters and 35 cats [difference = 25.... BINGO!!!]

So, there are 10 spinsters
Answer: A

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Re: The ratio of spinsters to cats is 2 to 7. If there are 25  [#permalink]

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New post 22 Jul 2018, 03:37
phoenix9801 wrote:
The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?

A. 10
B. 12
C. 15
D. 18
E. 27


Given ratio = S:C = 2:7.
The difference between the parts of the ratio = 7-2 = 5.
Since the actual difference between the number of cats and the number of spinsters is five times as great -- 25 -- each part of the ratio must be multiplied by a FACTOR OF 5:
S:C = (2*5) : (7*5) = 10:35, with the result that there are 25 more cats than spinsters.
Thus, S=10.


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Re: The ratio of spinsters to cats is 2 to 7. If there are 25  [#permalink]

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New post 22 Jul 2018, 05:15
Let Spinsters = s and Cats = c
s:c = 2:7
i.e. s/c=2/7
so 7s=2c

And c= 25 + s
Substituting, 7s = 50 + 2s
Therefore, s=10
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Re: The ratio of spinsters to cats is 2 to 7. If there are 25 &nbs [#permalink] 22 Jul 2018, 05:15
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The ratio of spinsters to cats is 2 to 7. If there are 25

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