document.write( "Question 1136973: After watching a major musical production at the theater, the patrons can purchase souvenirs. If a family purchases 6 t-shirts, the video, and a stuffed animal, their total is $135.
\n" ); document.write( "A couple buys 2 t-shirts, the video, and 5 stuffed animals for their nieces and spends $175. Another couple buys 2 t-shirts, the video, and a stuffed animal, and their total is $75. What is the cost of each item? \n" ); document.write( "
Algebra.Com's Answer #754831 by ankor@dixie-net.com(22740)\"\" \"About 
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After watching a major musical production at the theater, the patrons can purchase souvenirs.
\n" ); document.write( " If a family purchases 6 t-shirts, the video, and a stuffed animal, their total is $135.
\n" ); document.write( "A couple buys 2 t-shirts, the video, and 5 stuffed animals for their nieces and spends $175.
\n" ); document.write( " Another couple buys 2 t-shirts, the video, and a stuffed animal, and their total is $75.
\n" ); document.write( " What is the cost of each item?
\n" ); document.write( ":
\n" ); document.write( "let t = price of T shirts
\n" ); document.write( "let v = price of video
\n" ); document.write( "let a = price of stuffed animal
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement
\n" ); document.write( "\" If a family purchases 6 t-shirts, the video, and a stuffed animal, their total is $135.\"
\n" ); document.write( "6t + v + a = 135
\n" ); document.write( " \"A couple buys 2 t-shirts, the video, and 5 stuffed animals for their nieces and spends $175.\"
\n" ); document.write( "2t + v + 5a = 175
\n" ); document.write( " \"Another couple buys 2 t-shirts, the video, and a stuffed animal, and their total is $75.\"
\n" ); document.write( "2t + v + a = 75
\n" ); document.write( ":
\n" ); document.write( "Using the 2nd and 3rd equations find a
\n" ); document.write( "2t + v + 5a = 175
\n" ); document.write( "2t + v + a = 75
\n" ); document.write( "-----------------subtraction eliminates t and v, find a
\n" ); document.write( "4a = 100
\n" ); document.write( "a =100/4
\n" ); document.write( " a = $25 for the animal
\n" ); document.write( ":
\n" ); document.write( "Using the 1st and 2nd equations, substitute 25 for a
\n" ); document.write( "6t + v + 25 = 135
\n" ); document.write( "6t + v = 110, subtracted 25 from both sides
\n" ); document.write( "and
\n" ); document.write( "2t + v + 5(25) = 175
\n" ); document.write( "2t + v = 50, subtracted 125 from both sides
\n" ); document.write( ":
\n" ); document.write( "Using elimination on these two equations
\n" ); document.write( "6t + v = 110
\n" ); document.write( "2t + v = 50]
\n" ); document.write( "--------------subtraction eliminates v, find t
\n" ); document.write( "4t = 60
\n" ); document.write( "t = 60/4
\n" ); document.write( "t = $15 for T shirts
\n" ); document.write( ":
\n" ); document.write( "Find v using the 3rd equation,
\n" ); document.write( "2(15) + v + 25 = 75
\n" ); document.write( "v = 75 - 30 - 25
\n" ); document.write( "v = 75 - 55
\n" ); document.write( "v = $20 for each video
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solutions in the 1st equation
\n" ); document.write( "6(15) + 20 + 25 = 175 \n" ); document.write( "
\n" );