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Each Machine of type A has 3 steel parts and 2 chrome parts.

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Each Machine of type A has 3 steel parts and 2 chrome parts. [#permalink]

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Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 4 steel parts and 7 chrome parts. If a certain group of type A and type B machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group

A. 2
B. 3
C. 4
D. 6
E. 9
[Reveal] Spoiler: OA
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Re: No. of machines [#permalink]

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New post 14 Mar 2011, 14:57
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tonebeeze wrote:
Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 4 steel parts and 7 chrome parts. If a certain group of type A and type B machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group

a. 2
b. 3
c. 4
d. 6
e. 9


Given:
(i) \(3a+4b=20\) and (ii) \(2a+7b=22\), where \(a\) and \(b\) are # of type A and type B machines respectively.

Multiply (i) by 2 and (ii) by 3 and subtract: \((6a+21b)-(6a+8b)=66-40\) --> \(b=2\) --> \(a=4\) --> \(a+b=6\).

Answer: D.

Or you can notice that from (i) \(3a=20-4b\): 20 minus multiple of 4 to be a positive multiple of 3 \(b\) must be either 2 or 5 (which doesn't fit into the second equation) --> \(b=2\) --> \(a=4\) --> \(a+b=6\).

Answer: D.
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Re: No. of machines [#permalink]

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New post 14 Mar 2011, 21:20
Look at the below representation of the problem:
Steel Chrome total
A 3 2 20 >>no. of type A machines=20/5=4

B 4 7 22 >>no. of type B machines=22/11=2


So the answer is 6 i.e D.

Hope its clear .
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Re: No. of machines [#permalink]

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New post 14 Mar 2011, 21:40
Let there be x # of machine A and y # of machine B

So we have :

3x + 4y = 20

4x + 7y = 22

=> y = 2 and x = (20 - 8)/3 = 4

So total = 6, answer is D.
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Re: No. of machines [#permalink]

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New post 15 Mar 2011, 23:06
tonebeeze wrote:
Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 4 steel parts and 7 chrome parts. If a certain group of type A and type B machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group

a. 2
b. 3
c. 4
d. 6
e. 9



3a + 4b = 20 ......1

4a + 7b = 22.......2

solving (!) n (2)
b=2 a=4

thus total=6
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Re: No. of machines [#permalink]

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New post 02 Jun 2012, 14:54
We have ratios, so we can use unknown multiplier

3x + 2x = 20 ---> x=2

4x + 7x = 22 ----> x= 4

4+2=6 .........40 sec about
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Re: Each Machine of type A has 3 steel parts and 2 chrome parts. [#permalink]

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Re: Each Machine of type A has 3 steel parts and 2 chrome parts.   [#permalink] 23 Dec 2017, 03:00
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