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A garage has a stock of side mirrors. The ratio of right side mirrors

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A garage has a stock of side mirrors. The ratio of right side mirrors  [#permalink]

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06 Dec 2017, 04:37
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A garage has a stock of side mirrors. The ratio of right side mirrors to left side mirrors is 5:3. Iris, a garage worker, attaches pairs of left and right mirrors with an adhesive tape until no more pairs can be made. If 30 right mirrors are left unpaired, how many left and right mirrors are there in the stock?

A. 240
B. 120
C. 80
D. 75
E. 48

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Re: A garage has a stock of side mirrors. The ratio of right side mirrors  [#permalink]

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06 Dec 2017, 04:43
Tridhipal wrote:
A garage has a stock of side mirrors. The ratio of right side mirrors to left side mirrors is 5:3. Iris, a garage worker, attaches pairs of left and right mirrors with an adhesive tape until no more pairs can be made. If 30 right mirrors are left unpaired, how many left and right mirrors are there in the stock?

A. 240
B. 120
C. 80
D. 75
E. 48

$$\frac{right}{left}=\frac{5x}{3x}$$.

30 right mirrors are left unpaired means that there are 30 more right mirrors than left mirrors: $$right - left = 5x - 3x = 30$$ --> $$x = 15$$.

$$Total = 5x + 3x = 8x=8*15=120$$.

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Re: A garage has a stock of side mirrors. The ratio of right side mirrors  [#permalink]

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06 Dec 2017, 06:06
Tridhipal wrote:
A garage has a stock of side mirrors. The ratio of right side mirrors to left side mirrors is 5:3. Iris, a garage worker, attaches pairs of left and right mirrors with an adhesive tape until no more pairs can be made. If 30 right mirrors are left unpaired, how many left and right mirrors are there in the stock?

A. 240
B. 120
C. 80
D. 75
E. 48

Imo B

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Re: A garage has a stock of side mirrors. The ratio of right side mirrors  [#permalink]

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06 Dec 2017, 06:19
Tridhipal wrote:
A garage has a stock of side mirrors. The ratio of right side mirrors to left side mirrors is 5:3. Iris, a garage worker, attaches pairs of left and right mirrors with an adhesive tape until no more pairs can be made. If 30 right mirrors are left unpaired, how many left and right mirrors are there in the stock?

A. 240
B. 120
C. 80
D. 75
E. 48

You can also think in terms of ratios. The difference between the number of left mirrors and right mirrors is 2 on the ratio scale but actually it is 30. Hence the multiplier is 30/2 = 15
So total number of mirrors = (5 + 3) * 15 = 120

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Re: A garage has a stock of side mirrors. The ratio of right side mirrors  [#permalink]

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06 Dec 2017, 08:00
The nos are 5x, 3x
unpaired = 2x =30, hence x = 15
hence total = 8x = 120
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Re: A garage has a stock of side mirrors. The ratio of right side mirrors  [#permalink]

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03 Oct 2018, 15:08
Tridhipal wrote:
A garage has a stock of side mirrors. The ratio of right side mirrors to left side mirrors is 5:3. Iris, a garage worker, attaches pairs of left and right mirrors with an adhesive tape until no more pairs can be made. If 30 right mirrors are left unpaired, how many left and right mirrors are there in the stock?

A. 240
B. 120
C. 80
D. 75
E. 48

Excellent opportunity to use the k technique:

$$\left\{ \matrix{ {\rm{Right}} = 5k \hfill \cr {\rm{Left}} = 3k \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} \,\,\left( * \right)} \right)\,\,\,\,\,\,\,\,\,$$

$$\left( * \right)\,\,\,k = 2 \cdot \left( {3k} \right) - 5k = 2 \cdot {\mathop{\rm int}} - {\mathop{\rm int}} = {\mathop{\rm int}}$$

$$? = 8k\,\,\,\,\,\,\,\,\,\,\,$$

$$\left\{ \matrix{ \,\,3k\,\,{\rm{pairings}} \hfill \cr \,\,30 = \left( {5k - 3k} \right) = 2k\,\,{\rm{Right}}\,{\rm{unpaired}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,2k = 30\,\,\,\,\,\,\,\mathop \Rightarrow \limits_{{\rm{FOCUS}}\,!}^{ \cdot \,\,4} \,\,\,\,\,\,\,? = 8k = 4 \cdot 30 = 120 \hfill \cr} \right.\,\,\,\,\,\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: A garage has a stock of side mirrors. The ratio of right side mirrors  [#permalink]

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04 Oct 2018, 19:38
Tridhipal wrote:
A garage has a stock of side mirrors. The ratio of right side mirrors to left side mirrors is 5:3. Iris, a garage worker, attaches pairs of left and right mirrors with an adhesive tape until no more pairs can be made. If 30 right mirrors are left unpaired, how many left and right mirrors are there in the stock?

A. 240
B. 120
C. 80
D. 75
E. 48

We can let 5x = the number of right side mirrors and 3x = the number of left side mirrors. We can create the equation:

5x - 3x = 30

2x = 30

x = 15

Therefore, there are a total of 5(15) + 3(15) = 120 mirrors.

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Re: A garage has a stock of side mirrors. The ratio of right side mirrors  [#permalink]

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22 Oct 2018, 07:23
Tridhipal wrote:
A garage has a stock of side mirrors. The ratio of right side mirrors to left side mirrors is 5:3. Iris, a garage worker, attaches pairs of left and right mirrors with an adhesive tape until no more pairs can be made. If 30 right mirrors are left unpaired, how many left and right mirrors are there in the stock?

A. 240
B. 120
C. 80
D. 75
E. 48

R TO L
5 : 3
(5-3)= 30 pieces left

2 = 30
t/f 3 = ? .. by unitary method 5*30/2 = 75 = Right side mirrors

t/f 5=75
3=?
t/f 3*75/5 = 45= left side mirrors

left+right = 75+45 = 120 =B

(t/f = therefore)
best regards!
Re: A garage has a stock of side mirrors. The ratio of right side mirrors   [#permalink] 22 Oct 2018, 07:23
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