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a + b + c/2 = 60 –a – b + c/2 = –10
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17 May 2019, 02:11
17 May 2019, 02:11
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\(a + b + \frac{c}{2} = 60\)
\(–a – b + \frac{c}{2} = –10\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(–a – b + \frac{c}{2} = –10\)
Quantity A |
Quantity B |
b |
c |
A) Quantity A is greater.
B) Quantity 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: a + b + c/2 = 60 –a – b + c/2 = –10
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17 May 2019, 04:06
17 May 2019, 04:06
1
Carcass wrote:
\(a + b + \frac{c}{2} = 60\)
\(–a – b + \frac{c}{2} = –10\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(–a – b + \frac{c}{2} = –10\)
Quantity A |
Quantity B |
b |
c |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Given:
a + b + c/2 = 60
–a – b + c/2 = –10
ADD the two equations to get: c = 50
So, our two GIVEN equations become:
a + b + 50/2 = 60
–a – b + 50/2 = –10
Simplify:
a + b + 25.5 = 60
-a - b + 25.5 = -10
Simplify:
a + b = 34.5
-a - b = -35.5
At this point we need to recognize that these two equations are EQUIVALENT.
We can better see this if we take the BOTTOM equation and multiply both sides by -1 to get: a + b = 34.5, which is identical to the TOP equation.
There are infinitely many solutions to the equation a + b = 34.5
Here are two possible cases.
case i: a = 34.5 and b = 0
We get:
QUANTITY A: 0
QUANTITY B: 50
In this case, Quantity B is greater
case ii: a = -100 and b = 134.5
We get:
QUANTITY A: 134.5
QUANTITY B: 50
In this case, Quantity A is greater
Answer: D
Cheers,
Brent
Intern
Joined: 19 May 2019
Posts: 3
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Concentration: Healthcare, Strategy
Re: a + b + c/2 = 60 –a – b + c/2 = –10
[#permalink]
19 May 2019, 16:47
19 May 2019, 16:47
1
GreenlightTestPrep wrote:
Carcass wrote:
\(a + b + \frac{c}{2} = 60\)
\(–a – b + \frac{c}{2} = –10\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(–a – b + \frac{c}{2} = –10\)
Quantity A |
Quantity B |
b |
c |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Given:
a + b + c/2 = 60
–a – b + c/2 = –10
ADD the two equations to get: c = 50
So, our two GIVEN equations become:
a + b + 50/2 = 60
–a – b + 50/2 = –10
Simplify:
a + b + 25.5 = 60
-a - b + 25.5 = -10
Simplify:
a + b = 34.5
-a - b = -35.5
At this point we need to recognize that these two equations are EQUIVALENT.
We can better see this if we take the BOTTOM equation and multiply both sides by -1 to get: a + b = 34.5, which is identical to the TOP equation.
There are infinitely many solutions to the equation a + b = 34.5
Here are two possible cases.
case i: a = 34.5 and b = 0
We get:
QUANTITY A: 0
QUANTITY B: 50
In this case, Quantity B is greater
case ii: a = -100 and b = 134.5
We get:
QUANTITY A: 134.5
QUANTITY B: 50
In this case, Quantity A is greater
Answer: D
Cheers,
Brent
Why do you have 50/2 = 25.5? The final answer is correct but just curious how you arrived at that decimal.
