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

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Math Expert
Joined: 02 Sep 2009
Posts: 55718
Carina has 100 ounces of coffee divided into 5- and 10-ounce packages.  [#permalink]

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30 Jun 2015, 04:40
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:26) correct 20% (01:48) wrong based on 102 sessions

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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.

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Posts: 115
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Re: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages.  [#permalink]

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30 Jun 2015, 04:51
2
1
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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Updated on: 30 Jun 2015, 10:24
1
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

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Originally posted by GMATinsight on 30 Jun 2015, 10:23.
Last edited by GMATinsight on 30 Jun 2015, 10:24, 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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30 Jun 2015, 10:23
1
Solve using option ,
Option E out straightaway .
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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30 Jun 2015, 10:39
1
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
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Math Expert
Joined: 02 Sep 2009
Posts: 55718
Re: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages.  [#permalink]

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06 Jul 2015, 01:38
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.

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

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19 Mar 2016, 04:27
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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02 Jan 2018, 09:13
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Re: Carina has 100 ounces of coffee divided into 5- and 10-ounce packages.   [#permalink] 02 Jan 2018, 09:13
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