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5a + 3b = 2(a – b) and 6a + 4b = 12
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20 Jul 2019, 02:39
20 Jul 2019, 02:39
Expert Reply
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Question Stats:
83% (01:15) correct
16% (01:42) wrong based on 142 sessions
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\(5a + 3b = 2(a – b)\)
\(6a + 4b = 12\)
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.
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Re: 5a + 3b = 2(a – b) and 6a + 4b = 12
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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.
