GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
5a + 3b = 2(a – b) and 6a + 4b = 12
[#permalink]
20 Jul 2019, 02:39
20 Jul 2019, 02:39
Expert Reply
00:00
Question Stats:
82% (01:16) correct
17% (01:42) wrong based on 140 sessions
Hide Show timer Statistics
\(5a + 3b = 2(a – b)\)
\(6a + 4b = 12\)
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.
\(6a + 4b = 12\)
Quantity A |
Quantity B |
b |
-5 |
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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 5a + 3b = 2(a – b) and 6a + 4b = 12
[#permalink]
20 Jul 2019, 05:25
20 Jul 2019, 05:25
Carcass wrote:
\(5a + 3b = 2(a – b)\)
\(6a + 4b = 12\)
\(6a + 4b = 12\)
Quantity A |
Quantity B |
b |
-5 |
Given:
\(5a + 3b = 2(a – b)\)
\(6a + 4b = 12\)
Expand top equation:
\(5a + 3b = 2a – 2b\)
\(6a + 4b = 12\)
Simplify top equation. Take bottom equation and divide both sides by 2 to get:
\(3a + 5b = 0\)
\(3a + 2b = 6\)
Subtract the bottom equation from the top equation to get: \(3b = -6\)
Solve: \(b = -2\)
We get:
Quantity A: -2
Quantity B: -5
Answer: A
Cheers,
Brent
5a + 3b = 2(a b) and 6a + 4b = 12
[#permalink]
07 Jan 2024, 21:56
07 Jan 2024, 21:56
1
Solving both equations simultaneously to obtain the value of \(b\).
We first simplify \(5a+3b=2(a-b)\),
\(5a+3b=2(a-b) => 5a+3b=2a-2b => 5a-2a+3b+2b => 3a+5b=0\)
then,
\(3a+5b=0\)
\(6a+4b=12\)
\(3a+5b=0 \times 6\)
\(6a+4b=12 \times 3\)
\(18a+30b=0\)
\(18a+12b=36\)
Subtracting the second equation from the first, we get
\(18b = -36\)
\(b=\frac{-36}{18}\)
\(b=-2\)
Quantity A = \(- 2\)
Quantity B = \(- 5\)
Quantity A is greater.
We first simplify \(5a+3b=2(a-b)\),
\(5a+3b=2(a-b) => 5a+3b=2a-2b => 5a-2a+3b+2b => 3a+5b=0\)
then,
\(3a+5b=0\)
\(6a+4b=12\)
\(3a+5b=0 \times 6\)
\(6a+4b=12 \times 3\)
\(18a+30b=0\)
\(18a+12b=36\)
Subtracting the second equation from the first, we get
\(18b = -36\)
\(b=\frac{-36}{18}\)
\(b=-2\)
Quantity A = \(- 2\)
Quantity B = \(- 5\)
Quantity A is greater.
