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Carina has 100 ounces of coffee divided into 5- and 10-ounce packages.

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Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. [#permalink]

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Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?

A. 2
B. 4
C. 6
D. 8
E. 10

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. [#permalink]

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Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?

A. 2
B. 4
C. 6
D. 8
E. 10

Solution -

Lets say 5 and 10 ounce packages be x and y respectively.

Given that, 5x+10y=100 and x=y+2. What is the value of y.

Substituting the x in first equation, 5y+10+10y=100 ->y=6.
ANS C.
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Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. [#permalink]

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New post 30 Jun 2015, 09:23
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Bunuel wrote:
Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?

A. 2
B. 4
C. 6
D. 8
E. 10

Kudos for a correct solution.


One 10-Ounce package = Two 5-Ounce package

Let, a packages of 10-Ounce package are available
i.e. a 10-Ounce package = 2a 5-Ounce package
Total Coffee in (2a) 5-Ounce package = (2a)*5


then the No . of 5-Ounce packages available = (a+2)
Total Coffee in (a+2) 5-Ounce package = (a+2)*5

Total Coffee = (a+2)*5 + (2a)*5 = 100


i.e. 15a + 10 = 100
i.e. a = 6

Answer: option C
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Last edited by GMATinsight on 30 Jun 2015, 09:24, edited 1 time in total.

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Re: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. [#permalink]

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New post 30 Jun 2015, 09:23
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Solve using option ,
Option E out straightaway .
Start with middle value to be considered .
consider option D , then 10*8=80 and 5*4=20 but difference is not 2.
Consider option C , then 10*6=60 and 5*8=40 ... difference 8-6=2 .. hence this is answer
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Re: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. [#permalink]

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New post 30 Jun 2015, 09:39
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Let # 5 once package=x , # 10 once package =y
so we have 5x+10Y =100 ---1
and x=y+2 ---2
equating equation 1 & 2 we get y = 6
Hence answer is C
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Re: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. [#permalink]

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New post 06 Jul 2015, 00:38
Bunuel wrote:
Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?

A. 2
B. 4
C. 6
D. 8
E. 10

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

Let a = the number of 5-ounce packages.
Let b = the number of 10-ounce packages.

Carina has 100 ounces of coffee: 5a + 10b = 100
She has two more 5-ounce packages than 10-ounce packages: a = b + 2

Combine the equations by substituting the value of a from equation 2 into equation 1.
5(b + 2) + 10b = 100
b = 6.

Answer: C.
_________________

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: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. [#permalink]

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New post 19 Mar 2016, 03:27
Bunuel wrote:
Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?

A. 2
B. 4
C. 6
D. 8
E. 10

Kudos for a correct solution.

It is easier to plug in values in the option to get the answer.
A 4*5+2*10=40
B 6*5+4*10=70
C 8*5+6*10=100

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Re: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. [#permalink]

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Re: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages.   [#permalink] 02 Jan 2018, 08:13
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