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At a hobby store, the ratio of telescopes to microscopes is currently

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At a hobby store, the ratio of telescopes to microscopes is currently  [#permalink]

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New post 10 Apr 2018, 20:47
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A
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Question Stats:

87% (01:12) correct 13% (01:28) wrong based on 64 sessions

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At a hobby store, the ratio of telescopes to microscopes is currently 3:2. If 10 microscopes were to be sold, that ratio would then be 2:1. How many telescopes does the store have?

A. 15
B. 30
C. 45
D. 60
E. 75

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Re: At a hobby store, the ratio of telescopes to microscopes is currently  [#permalink]

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New post 10 Apr 2018, 22:01
Bunuel wrote:
At a hobby store, the ratio of telescopes to microscopes is currently 3:2. If 10 microscopes were to be sold, that ratio would then be 2:1. How many telescopes does the store have?

A. 15
B. 30
C. 45
D. 60
E. 75


As word problems involving a change in ratios can be confusing, we'll instead use the answers.
This is an Alternative approach.

Say the median, (C), were correct, that is there are 45 telescopes in the store.
Then there are 45/3*2 = 30 microscopes. Subtracting 10 gives a ratio of 45:20 which is not 2:1. No!
We need to make the ratio smaller so we'll choose a larger answer.
Say (D). Then there are 60/3*2 = 40 microscopes and subtracting 10 gives 60:30=2:1. Yes!

(D) is our answer.
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Re: At a hobby store, the ratio of telescopes to microscopes is currently  [#permalink]

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New post 10 Apr 2018, 23:45
1
i got Answer D.
3x/2x-10=2/1, we get x=20
Thus, the no. of telescopes=60
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At a hobby store, the ratio of telescopes to microscopes is currently  [#permalink]

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New post 12 Apr 2018, 09:01
\(\frac{t}{m}\) = \(\frac{3}{2}\) > 3m = 2t > m = \(\frac{2t}{3}\)

\(\frac{t}{(m-10)}\) = \(\frac{2}{1}\)

\(\frac{t}{((2t/3)-10)}\) = 2 > t = \(\frac{4t}{3}\) - 20 > 3t = 4t - 60 > t = 60 (Option D)
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Re: At a hobby store, the ratio of telescopes to microscopes is currently  [#permalink]

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New post 12 Apr 2018, 15:23
Bunuel wrote:
At a hobby store, the ratio of telescopes to microscopes is currently 3:2. If 10 microscopes were to be sold, that ratio would then be 2:1. How many telescopes does the store have?

A. 15
B. 30
C. 45
D. 60
E. 75



We are given that the ratio of telescopes to microscopes = 3x : 2x, so we can create the equation:

3x/(2x - 10) = 2/1

2(2x - 10) = 3x

4x - 20 = 3x

x = 20

So there are currently 3 x 20 = 60 telescopes.

Answer: D
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Re: At a hobby store, the ratio of telescopes to microscopes is currently &nbs [#permalink] 12 Apr 2018, 15:23
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