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# If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58452
If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?  [#permalink]

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19 Feb 2019, 21:55
00:00

Difficulty:

15% (low)

Question Stats:

87% (01:33) correct 13% (01:21) wrong based on 30 sessions

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If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?

A. −2
B. 0
C. 10
D. 17
E. 34

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Joined: 18 Aug 2017
Posts: 5020
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?  [#permalink]

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20 Feb 2019, 00:50
1
Bunuel wrote:
If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?

A. −2
B. 0
C. 10
D. 17
E. 34

a+b=12+2c
and
3*(a+b)+c=22
so
c=-2
IMO A
VP
Joined: 31 Oct 2013
Posts: 1465
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?  [#permalink]

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20 Feb 2019, 15:46
Bunuel wrote:
If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?

A. −2
B. 0
C. 10
D. 17
E. 34

Given ,

a + b - 2c = 12

a + b = 12 + 2c

again

3a + 3b + c = 22

3( a + b) + c = 22

3( 12 + 2c) + c = 22

36 + 6c + c = 22

7c = -14

c = -2.

If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?   [#permalink] 20 Feb 2019, 15:46
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