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If 5a – 3b = –9 and 3a + b = 31, then a + b =

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Bunuel
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If 5a – 3b = –9 and 3a + b = 31, then a + b = [#permalink] New post   03 Jun 2018, 11:53
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Question Stats:

88% (01:50) correct 12% (01:57) wrong based on 64 sessions
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If 5a – 3b = –9 and 3a + b = 31, then a + b =

A) –7

B) –3

C) 6

D) 13

E) 19
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E
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Re: If 5a – 3b = –9 and 3a + b = 31, then a + b = [#permalink] New post   03 Jun 2018, 12:48
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Bunuel wrote:
If 5a – 3b = –9 and 3a + b = 31, then a + b =

A) –7

B) –3

C) 6

D) 13

E) 19


Elimination method:-
Multiply equation (1) with 3 and equation (2) with 5, then subtracting (2) from (1), we have
3*(5a – 3b = –9) --------(1)
5*(3a + b = 31) --------(2)
(-) (-) (-)
.......................................................
-14b = -182
or, b=\(\frac{-182}{-14}\)=13

from (2) we have, 3a=31-b
or, a=\(\frac{(31-b)}{3}\)
Now substituting the value of b, we have
a=\(\frac{(31-13)}{3}\)=\(\frac{18}{3}\)=6

So, we have a+b=6+13=19.

Hence, Option (E) is the answer.
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If 5a – 3b = –9 and 3a + b = 31, then a + b = [#permalink] New post   03 Jun 2018, 20:01
Expert Reply
Bunuel wrote:
If 5a – 3b = –9 and 3a + b = 31, then a + b =

A) –7

B) –3

C) 6

D) 13

E) 19

Given:
5a – 3b = –9 ...(P)
3a + b = 31 ....(Q)

Multiply (Q) by 3 to get (R), then add (P) and (R)

5a – 3b = –9 ...(P)
9a + 3b = 93 ...(R)
-------------------
14a = 84
a = 6

Find b

From (Q): 3a + b = 31

(3)(6) + b = 31
b = (31-18) = 13

(a + b) = (6 + 13) = 19

Answer E
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Re: If 5a – 3b = –9 and 3a + b = 31, then a + b = [#permalink] New post   04 Jun 2018, 00:26
Bunuel wrote:
If 5a – 3b = –9 and 3a + b = 31, then a + b =

A) –7

B) –3

C) 6

D) 13

E) 19


Given: 5a – 3b = –9 and 3a + b = 31

Rearranging the second equation we get b = 31 - 3a

Substituting this value of b in the first equation.
5a - 3(31 - 3a) = -9 -> 14a - 93 = -9 -> 14a = 84 -> a = 6 | b = 31 - 18 = 13

Therefore, a+b = 6+13 = 19(Option E)
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If 5a − 3b = −9 and 3a + b = 31, then a + b = [#permalink] New post   Updated on: 28 Feb 2019, 11:07
5a-3b = -9.............(1)
3a+b = 31.............(2)

Multiply (1) by 3 and (2) by 5, then

15a-9b = -27
15a+5b = 155
subtract (1) from (2); 14b = 182, b = 13,
a = 6
a+b = 19

Originally posted by Chethan92 on 28 Feb 2019, 10:55.
Last edited by Chethan92 on 28 Feb 2019, 11:07, edited 1 time in total.
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Re: If 5a − 3b = −9 and 3a + b = 31, then a + b = [#permalink] New post   28 Feb 2019, 11:03
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Afc0892 wrote:
5a-3b = -9.............(1)
3a+b = 31.............(2)

Multiply (1) by 3 and (2) by 5, then

15a-9b = -27
15a+5b = 155
add both, -4b = 128, b = -32,
a = 21
a+b = -11

Bunuel sir, can you check the options?


If you add you'd get 30a -4b = 128. You should subtract.
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Re: If 5a − 3b = −9 and 3a + b = 31, then a + b = [#permalink] New post   28 Feb 2019, 11:05
Bunuel wrote:
Afc0892 wrote:
5a-3b = -9.............(1)
3a+b = 31.............(2)

Multiply (1) by 3 and (2) by 5, then

15a-9b = -27
15a+5b = 155
add both, -4b = 128, b = -32,
a = 21
a+b = -11

Bunuel sir, can you check the options?


If you add you'd get 30a -4b = 128. You should subtract.


oh yes. silly mistake :(
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Re: If 5a − 3b = −9 and 3a + b = 31, then a + b = [#permalink] New post   28 Feb 2019, 11:51
Bunuel wrote:
If 5a − 3b = −9 and 3a + b = 31, then a + b =

A. −7
B. −3
C. 6
D. 13
E. 19


Given,

3a + b = 31

b = 31 - 3a.

again

5a - 3b = -9

5a - 3(31 - 3a) = -9

5a - 93 + 9a = -9

14a = 84.

a = 6.

we know,

3a + b = 31

3*6 + b = 31

18 + b = 31

b = 31 - 18

b = 13.

Now we have ,

a = 6

b = 13.

a + b = 6 +13 = 19.

E is the correct answer.
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Re: If 5a − 3b = −9 and 3a + b = 31, then a + b = [#permalink] New post   28 Feb 2019, 12:19
Is there a shorter solution?
My solution:
1) add two equations
5a - 3b + 3a + b = 31 - 9
8a - 2b = 22
4a - b = 11 => b = 4a - 11

2) find a and b by plugging b into any of them
5a - 12a + 33 = - 9
7a = 42
a = 6 => b = 31-18 = 13

Answer: a+b = 13+6 = 19. Choice E
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Re: If 5a − 3b = −9 and 3a + b = 31, then a + b = [#permalink] New post   01 Mar 2019, 04:01
Bunuel wrote:
If 5a − 3b = −9 and 3a + b = 31, then a + b =

A. −7
B. −3
C. 6
D. 13
E. 19


solve for two given eqns

5a − 3b = −9 and 3a + b = 31
we get a = 6
and b = 13
a+b=19
IMO E
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Re: If 5a − 3b = −9 and 3a + b = 31, then a + b = [#permalink]
01 Mar 2019, 04:01
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