document.write( "Question 697798: Please help me solve this word problem:
\n" ); document.write( " In a souvenir shop, Jodi purchased 2 small picture frames and 1 large one for $28. Mike bought 3 medium-size frames and 2 large ones for $56. Shelly bought a small, a medium, and a large frame for $30. Write and solve a system of equations to find the price of each picture frame.\r
\n" ); document.write( "\n" ); document.write( " So far I have 2x+z=28 and 3y+2z=56 and x+y+z=30 with x being equal to the price of a small frame, y being the price of a medium one, and z being the price of a large one but I do not know how to solve it. \n" ); document.write( "
Algebra.Com's Answer #430303 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
In a souvenir shop, Jodi purchased 2 small picture frames and 1 large one for $28.
\n" ); document.write( " Mike bought 3 medium-size frames and 2 large ones for $56.
\n" ); document.write( " Shelly bought a small, a medium, and a large frame for $30.
\n" ); document.write( " Write and solve a system of equations to find the price of each picture frame.
\n" ); document.write( ":
\n" ); document.write( "You have to jump thru a few hoops to get to this one, elimination & substitution
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each person's purchase using your variables
\n" ); document.write( "2x + 0y + z = 28
\n" ); document.write( "0x + 3y + 2z = 56
\n" ); document.write( "x + y + z = 30
\n" ); document.write( ":
\n" ); document.write( "Subtract the 3rd equation from the 1st
\n" ); document.write( "2x + 0y + z = 28
\n" ); document.write( "x + y + z = 30
\n" ); document.write( "--------------------eliminates z
\n" ); document.write( "x - y = -2
\n" ); document.write( "x = y - 2
\n" ); document.write( ":
\n" ); document.write( "Rearrange the 2nd equation
\n" ); document.write( "3y + 2z = 56
\n" ); document.write( "2z = (56-3y)
\n" ); document.write( "z = \"%2856-3y%29%2F2\"
\n" ); document.write( ":
\n" ); document.write( "in the first equation
\n" ); document.write( "2x + 0y + z = 28
\n" ); document.write( "replace x and z
\n" ); document.write( "2(y-2) + \"%2856-3y%29%2F2\" = 28
\n" ); document.write( "2y - 4 + \"%2856-3y%29%2F2\" = 28
\n" ); document.write( "multiply by 2
\n" ); document.write( "2(2y-4) + 56 - 3y = 56
\n" ); document.write( "4y - 8 + 56 - 3y = 56
\n" ); document.write( "4y - 3y + 48 = 56
\n" ); document.write( "y = 56 - 48
\n" ); document.write( "y = $8 for the medium frame
\n" ); document.write( ":
\n" ); document.write( "find z using the 2nd equation
\n" ); document.write( "3(8) + 2z = 56
\n" ); document.write( "24 + 2z = 56
\n" ); document.write( "2z = 56 - 24
\n" ); document.write( "2z = 32
\n" ); document.write( "z = $16 for the large frame
\n" ); document.write( ":
\n" ); document.write( "You can use the 3rd equation to find x now\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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