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

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Math Expert
Joined: 02 Sep 2009
Posts: 47219
At a hobby store, the ratio of telescopes to microscopes is currently  [#permalink]

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10 Apr 2018, 21:47
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Difficulty:

25% (medium)

Question Stats:

81% (01:04) correct 19% (01:26) wrong based on 58 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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10 Apr 2018, 23:01
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!

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Joined: 31 Jul 2017
Posts: 11
Re: At a hobby store, the ratio of telescopes to microscopes is currently  [#permalink]

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11 Apr 2018, 00:45
1
3x/2x-10=2/1, we get x=20
Thus, the no. of telescopes=60
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Joined: 22 Jun 2017
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Location: Brazil
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At a hobby store, the ratio of telescopes to microscopes is currently  [#permalink]

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12 Apr 2018, 10:01
$$\frac{t}{m}$$ = $$\frac{3}{2}$$ > 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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12 Apr 2018, 16:23
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.

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Re: At a hobby store, the ratio of telescopes to microscopes is currently &nbs [#permalink] 12 Apr 2018, 16:23
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