Four friends, Charles, Mike, Brian, and John, went on a shopping trip. If Mike spent $400 more than Brian did, John spent $1200 less than Charles did, and Charles spent $400 more than Mike did, how many more dollars did Brian spend than John did?
A. $400
B. $600
C. $800
D. $1000
E. $1200
The OA is A.
If Mike spent $400 more than Brian, this can be written like M = B + 400 (1).
If John spent $1200 less than Charles, this can be written like J = C - 1200 (2).
If Charles spent $400 more than Mike, this can be written like C = M + 400 (3).
Then, I need to find how many more dollars did Brian spent than John, Can I write this like B - J = $?
From (1), B = M - 400
Then (1) - (2),
B - J = M - 400 - C + 1200 = M - C + 800 (4).
Then, (3) into (4), B -J = M - M - 400 + 800, finally, B - J = 400. Right?
Please, can any expert explain this PS question for me? I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
Four friends, Charles, Mike, Brian, and John, went on a...
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Hi swerve,Four friends, Charles, Mike, Brian, and John, went on a shopping trip. If Mike spent $400 more than Brian did, John spent $1200 less than Charles did, and Charles spent $400 more than Mike did, how many more dollars did Brian spend than John did?
A. $400
B. $600
C. $800
D. $1000
E. $1200
The OA is A.
If Mike spent $400 more than Brian, this can be written like M = B + 400 (1).
If John spent $1200 less than Charles, this can be written like J = C - 1200 (2).
If Charles spent $400 more than Mike, this can be written like C = M + 400 (3).
Then, I need to find how many more dollars did Brian spent than John, Can I write this like B - J = $?
From (1), B = M - 400
Then (1) - (2),
B - J = M - 400 - C + 1200 = M - C + 800 (4).
Then, (3) into (4), B -J = M - M - 400 + 800, finally, B - J = 400. Right?
Please, can any expert explain this PS question for me? I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
Let's take a look at your question.
The approach you used is absolutely correct. But we can solve it Just by adding up all three equations.
$$M=B+400\ ...\left(i\right)$$
$$J=C-1200\ ...\left(ii\right)$$
$$C=M+400...\left(iii\right)$$
Adding Eq(i), (ii) and (iii), we get:
$$M+J+C=B+400+C-1200+M+400$$
$$M+J+C=B+C+M-400$$
$$J=B-400$$
$$B-J=400$$
Therefore, Option A is correct.
Hope it helps.
I am available if you'd like any follow up.
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Mike spent $400 more than Brian did.swerve wrote:Four friends, Charles, Mike, Brian, and John, went on a shopping trip. If Mike spent $400 more than Brian did, John spent $1200 less than Charles did, and Charles spent $400 more than Mike did, how many more dollars did Brian spend than John did?
A. $400
B. $600
C. $800
D. $1000
E. $1200
Let B=1000, implying that M = 1000+400 = 1400.
Charles spent $400 more than Mike did.
Since M=1400, C = 1400+400 = 1800.
John spent $1200 less than Charles did.
Since C=1800, J = 1800-1200 = 600.
How many more dollars did Brian spend than John did?
B-J = 1000-600 = 400.
The correct answer is A.
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We can create the equations:swerve wrote:Four friends, Charles, Mike, Brian, and John, went on a shopping trip. If Mike spent $400 more than Brian did, John spent $1200 less than Charles did, and Charles spent $400 more than Mike did, how many more dollars did Brian spend than John did?
A. $400
B. $600
C. $800
D. $1000
E. $1200
M = B + 400
and
J = C - 1200
and
C = M + 400
Adding equations 2 and 3, we have:
J + C = C + M - 800
J = M - 800
Adding M = B + 400 and J = M - 800, we have:
M + J = B + M - 400
J = B - 400
J + 400 = B
We see that Brian spent $400 more than John.
Answer: A
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