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M16-24

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M16-24  [#permalink]

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New post 15 Sep 2014, 23:59
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  25% (medium)

Question Stats:

83% (02:35) correct 17% (02:53) wrong based on 42 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

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Re M16-24  [#permalink]

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New post 15 Sep 2014, 23:59
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M16-24  [#permalink]

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New post 03 Jun 2017, 08:50
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, 10:05
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, 10:55
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, 22:58
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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?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M16-24  [#permalink]

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New post 05 Feb 2019, 03:12
Brilliant. Thanks a ton!
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Re: M16-24   [#permalink] 05 Feb 2019, 03:12
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