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3a + 2b = 20 and 2a + 3b = 5

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3a + 2b = 20 and 2a + 3b = 5 [#permalink] New post 20 May 2018, 16:57
Expert's post
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Question Stats:

66% (01:04) correct 33% (00:56) wrong based on 59 sessions
3a + 2b = 20 and 2a + 3b = 5

Quantity A
Quantity B
a+b
a


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: 3a + 2b = 20 and 2a + 3b = 5 [#permalink] New post 23 May 2018, 09:39
Adding both equations,

5(a+b) = 25
a+b = 5 (eq1)
3a + 2b = 20

Multiplying eq1 with 2
2a+2b = 10
3a + 2b = 20

Substracting eq 2 from 1, a = 10

Hence B
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Re: 3a + 2b = 20 and 2a + 3b = 5 [#permalink] New post 31 May 2020, 06:28
Expert's post
sandy wrote:
3a + 2b = 20 and 2a + 3b = 5

Quantity A
Quantity B
a+b
a



There are two primary ways to solve systems of equations

1) Substitution method
2) Elimination method

And most cases (and especially in this case), the elimination method will be faster.

Take:
3a + 2b = 20
2a + 3b = 5
Add the equations to get: 5a + 5b = 25
Divide both sides by 5 to get: a + b = 5


Now take:
3a + 2b = 20
2a + 3b = 5

Multiply both sides of the TOP equation by 3, and multiply both sides of the BOTTOM equation by 2 to get:
9a + 6b = 60
4a + 6b = 10

Subtract the bottom equation from the top equation to get: 5a = 50, which means a = 10

We now have:
QUANTITY A: 5
QUANTITY B: 10

Answer: B

Cheers,
Brent
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Re: 3a + 2b = 20 and 2a + 3b = 5 [#permalink] New post 22 Jun 2020, 22:05
here we 2 equations.
1- 3a +2b=20
2- 2a +3b=5
Subtract both
a-b=15.
Ok we have
QA a+B QB a
subtract a from both to get
QA B
QB 0
and we know that a-b=15 and a here must be greater than b to get positive number.
hence the answer is B
any suggestion for my approach will be appreciated
Re: 3a + 2b = 20 and 2a + 3b = 5   [#permalink] 22 Jun 2020, 22:05
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3a + 2b = 20 and 2a + 3b = 5

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