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# M16-24

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Math Expert
Joined: 02 Sep 2009
Posts: 56304

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16 Sep 2014, 00:59
00:00

Difficulty:

25% (medium)

Question Stats:

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

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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 _________________ Math Expert Joined: 02 Sep 2009 Posts: 56304 Re M16-24 [#permalink] ### Show Tags 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 $$15*0.2 + 5*0.3 = 4.5$$.

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Intern
Joined: 25 Jan 2016
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Location: United States (NJ)
GPA: 2.34
WE: Analyst (Commercial Banking)

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03 Jun 2017, 09:50
Hi,

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

Retired Moderator
Joined: 22 Aug 2013
Posts: 1435
Location: India

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

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

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
Intern
Joined: 04 Sep 2018
Posts: 36
GPA: 3.33

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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??
Math Expert
Joined: 02 Sep 2009
Posts: 56304

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23 Jan 2019, 23:58
1
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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Joined: 04 Sep 2018
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05 Feb 2019, 04:12
Brilliant. Thanks a ton!
Intern
Joined: 22 Sep 2016
Posts: 45
Location: India
Concentration: International Business, General Management
GMAT 1: 680 Q44 V39

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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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Spiritual Yoda
Re M16-24   [#permalink] 22 Mar 2019, 05:48
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# M16-24

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