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3a + 2b = 20 and 2a + 3b = 5
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20 May 2018, 16:57
20 May 2018, 16:57
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3a + 2b = 20 and 2a + 3b = 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.
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.
Re: 3a + 2b = 20 and 2a + 3b = 5
[#permalink]
23 May 2018, 09:39
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
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
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31 May 2020, 06:28
31 May 2020, 06:28
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
