document.write( "Question 1205627: A travel agency offers two Boston trips. Plan A includes hotel accommodations for three nights and two pairs of baseball tickets for $645. Plan B includes hotel accommodations for five nights and four pairs of baseball tickets for $1135. a. Let x represent the cost of one night’s hotel stay and y represent the cost of one pair of baseball tickets. Write a system of equations you could use to solve this problem for the cost of the hotel and baseball tickets. \n" ); document.write( "
Algebra.Com's Answer #842548 by Theo(13342)![]() ![]() You can put this solution on YOUR website! x = number of nights at a hotel. \n" ); document.write( "y = number of pairs of baseball tickets.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "option A has 3 nights and 2 pairs of tickets. \n" ); document.write( "option B has 5 nights and 4 pairs of tickets.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "two equations that need to be solved simultaneously are:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "3x + 2y = 645 for option A. \n" ); document.write( "5x + 4y = 1135 for option B.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "multiply both sides of the first equation by 2 and leave the second equation as is to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "6x + 4y = 1290 \n" ); document.write( "5x + 4y = 1135\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "subtract the second equation from the first to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "x = 155\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solve for y in the first equation to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "6*155 + 4y = 1290 \n" ); document.write( "4y = 1290 - 930 = 360 \n" ); document.write( "y = 360/4 = 90\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you have x = 155 and y = 90 \n" ); document.write( "that's 155 a night at a hotel and 90 for a pair of tickets. \n" ); document.write( "that's your solution.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you can confirm by replacing x with 155 and y with 90 in your two original equations.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you will get 3*155 + 2 * 90 = 645 and you will get 5*155 + 4*90 = 1135, as i did.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |