document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #502859 by Theo(13342)\"\" \"About 
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let A equal the running time of movie A.
\n" ); document.write( "let B equal the running time of movie B.
\n" ); document.write( "formulas becomes:
\n" ); document.write( "A = 2B + 31
\n" ); document.write( "3B - A = 63
\n" ); document.write( "these are 2 equations that need to be solved simultaneously to find the common solution for both A and B.
\n" ); document.write( "you can solve them by either substitution or by elimination or by graphing or by a fourth method which i will use today.
\n" ); document.write( "the fourth method solves for A in both equations.
\n" ); document.write( "the first equation is already solved for A.
\n" ); document.write( "the second equation is solved for A as follows:
\n" ); document.write( "start with:
\n" ); document.write( "3B - A = 63
\n" ); document.write( "add A to both sides of the equation to get:
\n" ); document.write( "3B = A + 63
\n" ); document.write( "subtract 63 from both sides of the equation to get:
\n" ); document.write( "3B - 63 = A
\n" ); document.write( "commute this equation (switch sides) to get:
\n" ); document.write( "A = 3B - 63
\n" ); document.write( "you now have 2 equations that equal to A.
\n" ); document.write( "you now have:
\n" ); document.write( "A = 2B + 31
\n" ); document.write( "A = 3B - 63
\n" ); document.write( "since both expressions on the right side of the equqtions are equal to A, you can set them equal to each other to get:
\n" ); document.write( "2B + 31 = 3B - 63.
\n" ); document.write( "now all you have to do is solve for B and then solve for A.
\n" ); document.write( "start with:
\n" ); document.write( "2B + 31 = 3B - 63
\n" ); document.write( "subtract 2B from both sides of the equation to get:
\n" ); document.write( "31 = B - 63
\n" ); document.write( "add 63 to both sides of the equation to get:
\n" ); document.write( "B = 31 + 63 which results in:
\n" ); document.write( "B = 94
\n" ); document.write( "you can now solve for A in either of the original equations.
\n" ); document.write( "start with:
\n" ); document.write( "A = 2B + 31
\n" ); document.write( "replace B with 94 to get:
\n" ); document.write( "A = 2 * 94 + 31
\n" ); document.write( "simplify to get:
\n" ); document.write( "A = 219
\n" ); document.write( "the solution to your problem is:
\n" ); document.write( "A = 219
\n" ); document.write( "B = 94
\n" ); document.write( "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.
\n" ); document.write( "movie A running time is 31 minutes more than twice the running time for movie B.
\n" ); document.write( "2 * 94 = 188 + 31 = 219 which is equal to the running time for movie A, so the first statement is true.
\n" ); document.write( "If the running time for movie A is subtracted from triple the running time for movie B, the result is 63 minutes.
\n" ); document.write( "3 * 94 = 282
\n" ); document.write( "subtract 219 from 282 and you get 63, so the second statement is also true.
\n" ); document.write( "the solution is confirmed to be good for both equations.
\n" ); document.write( "the solution is:
\n" ); document.write( "running time for movie A is 219 minutes.
\n" ); document.write( "running time for movie B is 94 minutes.\r
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