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In a certain district, the ratio of the number of registered

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Re: In a certain district, the ratio of the number of registered [#permalink]

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New post 10 Jun 2016, 10:48
Walkabout wrote:
In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?

(A) 100
(B) 300
(C) 400
(D) 1,000
(E) 2,500


The fractional ratio indicates that for every 3 Republicans, there are 5 Democrats, a ratio of 3 : 5. We first set up this ratio of registered Republicans to registered Democrats using a variable multiplier:

Republicans: Democrats = 3x : 5x

We are given that 600 additional Republicans and 500 additional Democrats registered and that the new ratio of Republicans to Democrats was 4 to 5. This means that the new number of Republicans can be expressed as (3x + 600), and the new number of Democrats can be expressed as (5x + 500). We can put all this into an equation:

R/D  (3x+600)/(5x+500) = 4/5

After cross multiplying we have:

5(3x+600) = 4(5x+500)

15x + 3,000 = 20x + 2,000

1,000 = 5x

x = 200

Thus after the registration we have the following:

Democrats = (5 × 200) + 500 = 1,500

Republicans = (3 × 200) + 600 = 1,200

There are 1,500 – 1,200 = 300 more Democrats than Republicans.

Answer B.
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New post 27 Oct 2016, 08:20
Bunuel Can you please guide where I am getting wrong ?

R/D = 3/5 -----(1)

R+600 / D+500 = 4/5 ----(2)

Solving (2) we get

1000 = 4D - 5R

Substitute value of R from (1)

1000 = 4D - 5* (3D/5)

D = 1000

Hence R = 600

So difference should be 400 ??

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New post 27 Oct 2016, 09:05
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The difference of 400 is before the new registrations. But the problems asks for "After these (new) registrations..." So the new number of registered Republicans is 600 + 600 = 1200, and the new number of registered Democrats is 1000 + 500 = 1500. So the difference is 300.

Does that make sense?
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New post 27 Oct 2016, 09:25
ScottTargetTestPrep wrote:
The difference of 400 is before the new registrations. But the problems asks for "After these (new) registrations..." So the new number of registered Republicans is 600 + 600 = 1200, and the new number of registered Democrats is 1000 + 500 = 1500. So the difference is 300.

Does that make sense?


I agree to your explanation as its evident from the answer.

My query is algebraically where I am getting wrong? Is it that at the time if expressing a Q into ratios , we need to provide a constant 'k' or 'x' everytime
What is the significance of this constant?

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New post 31 Oct 2016, 07:46
I think you're getting confused with the variables that you created. When you make up variables in your equation, you need to know what those variables stand for - what they represent.. For example, what does the variable D correspond to? Right? Otherwise, your algebra looks fine. You just have to be careful to answer the question that is being asked. I hope this helps...
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In a certain district, the ratio of the number of registered [#permalink]

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New post 31 Oct 2016, 18:54
Walkabout wrote:
In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?

(A) 100
(B) 300
(C) 400
(D) 1,000
(E) 2,500


let t=total original registrations
3/8*t+600=4/9*(t+1100)
t=1600
t+1100=2700 revised total
5/9*2700=1500 democrats
4/9*2700=1200 republicans
1500-1200=300
B

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Re: In a certain district, the ratio of the number of registered [#permalink]

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New post 03 Nov 2017, 06:24
Does anybody know a solution with the ratio box?

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Re: In a certain district, the ratio of the number of registered   [#permalink] 03 Nov 2017, 06:24

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