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M16-24

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M16-24  [#permalink]

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New post 16 Sep 2014, 00:59
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

84% (02:32) correct 16% (02:53) wrong based on 45 sessions

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Math Expert
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Re M16-24  [#permalink]

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New post 16 Sep 2014, 00:59
Official Solution:

Ten cups and twenty glasses cost $8. If ten glasses and twenty cups cost $7, how much do fifteen cups and five glasses cost?

A. $3.5
B. $4.5
C. $5.0
D. $5.5
E. $6.5


Let's denote the price of one cup as \(C\) and the price of one glass as \(G\). Compose the following system of equations:
\(10C + 20G = 8\)
\(10G + 20C = 7\)

Solving this system, we get \(G = 0.3\), \(C = 0.2\). Hence, fifteen cups and five glasses cost \(15*0.2 + 5*0.3 = 4.5\).


Answer: B
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Re: M16-24  [#permalink]

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New post 03 Jun 2017, 09:50
Hi,

Can you please post the steps to solve this system of equations?

Thanks for your help in advance
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Re: M16-24  [#permalink]

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New post 03 Jun 2017, 11:05
Prostar wrote:
Hi,

Can you please post the steps to solve this system of equations?

Thanks for your help in advance


Hi. Let me try. Let G be the cost of one glass and let C be the cost of one cup. So we have:

20G + 10C = 8
10G + 20C = 7.. we have to find 5G + 15C

We can add the two given equations, so we get:
30G + 30C = 15.. Now divide both sides by 30, we get: G + C = 1/2 Or G = 1/2 - C

We can now substitute this value of G = 1/2-C in the first equation so we get:
20(1/2 - C) + 10C = 8 or 10 - 20C + 10C = 8 or 2 = 10C or C=1/5

WE have C, we can calculate G = 1/2 - C = 1/2 - 1/5 = 3/10

We now have G and C, we can calculate 5G + 15C = 5*3/10 + 15*1/5 = 1.5 + 3 = 4.5
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Re: M16-24  [#permalink]

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New post 23 Jan 2019, 11:55
Bunnel, Can you please help explain how you were able to get G=0.3, C=0.2 from the above equations??
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Re: M16-24  [#permalink]

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New post 23 Jan 2019, 23:58
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nust2017 wrote:
Bunnel, Can you please help explain how you were able to get G=0.3, C=0.2 from the above equations??


We have two distinct linear equations with two unknowns:
\(10C + 20G = 8\)
\(20C + 10G = 7\)

Multiply the first equation by 2 to get \(20C + 40G = 16\)

Now, subtract the second equation from the above: \(30G=9\) --> \(G=0.3\). Finally, plug this into either of the equations to get \(C=0.2\).

Does this make sense?
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Re: M16-24  [#permalink]

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New post 05 Feb 2019, 04:12
Brilliant. Thanks a ton!
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Re M16-24  [#permalink]

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New post 22 Mar 2019, 05:48
I think this is a poor-quality question and I agree with explanation. The overall system average response time seems to be inflated (very high). Are you sure that the logic removes the outliers while calculating the average?
It will be great if a standard response time is given for the right comparison.
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Re M16-24   [#permalink] 22 Mar 2019, 05:48
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