SOLUTION: the running time for movie A is 31 minutes more than twice the running time for movie B. If the running time for movie A is subtracted from triple the running time for movie B, the

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Question 834201: the running time for movie A is 31 minutes more than twice the running time for movie B. If the running time for movie A is subtracted from triple the running time for movie B, the result is 63 minutes. Find the running times for each movie
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
the running time for movie A is 31 minutes more than twice the running time for movie B. If the running time for movie A is subtracted from triple the running time for movie B, the result is 63 minutes. Find the running times for each movie
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Equations:
A = 2B+31
3B-A = 63
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Substitute for "A" and solve for "B":
3B -(2B+31) = 63
3B - 2B - 31 = 63
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B = 94 minutes
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A = 2B+31 = 2*94+31 = 219 minutes
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Cheers,
Stan H.
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Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let A equal the running time of movie A.
let B equal the running time of movie B.
formulas becomes:
A = 2B + 31
3B - A = 63
these are 2 equations that need to be solved simultaneously to find the common solution for both A and B.
you can solve them by either substitution or by elimination or by graphing or by a fourth method which i will use today.
the fourth method solves for A in both equations.
the first equation is already solved for A.
the second equation is solved for A as follows:
start with:
3B - A = 63
add A to both sides of the equation to get:
3B = A + 63
subtract 63 from both sides of the equation to get:
3B - 63 = A
commute this equation (switch sides) to get:
A = 3B - 63
you now have 2 equations that equal to A.
you now have:
A = 2B + 31
A = 3B - 63
since both expressions on the right side of the equqtions are equal to A, you can set them equal to each other to get:
2B + 31 = 3B - 63.
now all you have to do is solve for B and then solve for A.
start with:
2B + 31 = 3B - 63
subtract 2B from both sides of the equation to get:
31 = B - 63
add 63 to both sides of the equation to get:
B = 31 + 63 which results in:
B = 94
you can now solve for A in either of the original equations.
start with:
A = 2B + 31
replace B with 94 to get:
A = 2 * 94 + 31
simplify to get:
A = 219
the solution to your problem is:
A = 219
B = 94
this means that the running time for movie A is equal to 219 minutes while the running time for movie B is equal to 94 minutes.
movie A running time is 31 minutes more than twice the running time for movie B.
2 * 94 = 188 + 31 = 219 which is equal to the running time for movie A, so the first statement is true.
If the running time for movie A is subtracted from triple the running time for movie B, the result is 63 minutes.
3 * 94 = 282
subtract 219 from 282 and you get 63, so the second statement is also true.
the solution is confirmed to be good for both equations.
the solution is:
running time for movie A is 219 minutes.
running time for movie B is 94 minutes.