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# Company S produces two kinds of stereos: basic and deluxe.

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Manager
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Company S produces two kinds of stereos: basic and deluxe. [#permalink]

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08 Jan 2008, 08:07
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by
Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many
hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of
hours it took to produce the deluxe stereos last month was what fraction of the total
number of hours it took to produce all the stereos?

A.7/17
B.14/31
C. 7/15
D.17/35
E.1/2
Director
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08 Jan 2008, 08:48
10 were basic
5 were deluxe

10x for basic
5(7/5)x = 7x for deluxe

7/(10+7) = 7/17

SVP
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08 Jan 2008, 13:17
basic = 2/3*t , deluxe = 1/3*t where t=total number of stereos made

total time = (2/3t)x + (1/3t)(7/5x) where x=amount of time to make one basic stereo

fraction of time is second term in equation above divided by the sum of the two terms above.

expand and simplify to get 7/17
Director
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09 Jan 2008, 01:25
JCLEONES wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by
Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many
hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of
hours it took to produce the deluxe stereos last month was what fraction of the total
number of hours it took to produce all the stereos?

A.7/17
B.14/31
C. 7/15
D.17/35
E.1/2

A.

Assume company produced 9 stereos last mo.
Basic = 6
Del. = 3
Assume it takes 5 hrs to produce basic
Therefore, 7/5*5 = 7 hrs to produce del.

Time spent producing basic = 6*5 = 30
Time spend producing del. = 7*3 = 21
Required ratio = 21/51 = 7/17
Director
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09 Jan 2008, 03:13
Nd*td/(Nd*td+Nb*tb)=1/[1+((Nb*tb)/(Nd*td))]=1/[1+2*(5/7)]=7/17
Manager
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09 Jan 2008, 10:20
eschn3am wrote:
10 were basic
5 were deluxe

10x for basic
5(7/5)x = 7x for deluxe

7/(10+7) = 7/17

I solved correctly (A) using fractions ~ 3.5 min.
I have to say, picking numbers make a difference here, at least for me. (less than 2 min.)

how do you know to use the "picking numbers" method?
how do you choose the right numbers?
Director
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09 Jan 2008, 10:43
GGUY wrote:
eschn3am wrote:
10 were basic
5 were deluxe

10x for basic
5(7/5)x = 7x for deluxe

7/(10+7) = 7/17

I solved correctly (A) using fractions ~ 3.5 min.
I have to say, picking numbers make a difference here, at least for me. (less than 2 min.)

how do you know to use the "picking numbers" method?
how do you choose the right numbers?

I'm weird in the sense that I never follow a set guideline or idea on how things should be solved. I look at a problem and just know how I'm going to attack it (it's not always the best way, but this strategy has worked well for me thus far).

In this case I saw that we were dealing with 2/3 of the stereos being basic and 1/3 being deluxe. Using this information alone I would choose a multiple of 3 (like 6, where 4 stereos would be basic and 2 would be deluxe).

However, I kept reading and saw that we were also dealing with time taking (7/5x) time to build them so I wanted to find a number that was a multiple of five to get rid of that fraction easily.

I just combined the two ideas and came up with 15 because it's the first number divisible by both 3 and 5.

Basically I just choose numbers that cancel out denominators wherever possible. Hope this helps!
Manager
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09 Jan 2008, 19:36
I also like plugging in on these types of questions. But sometimes it does make sense to use algebra, just depends how you see the problem.
Re: Work problem S23_17   [#permalink] 09 Jan 2008, 19:36
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