document.write( "Question 1208974: While waiting for your car to be fixed, you and your friends go to Dim Sum Restaurant for food
\n" ); document.write( "(the popcorn and pretzels were not enough). All small dishes cost the same and all large dishes
\n" ); document.write( "cost the same. Before tip, your bill of 3 small dishes and 5 large dishes was $28.20. A bill at
\n" ); document.write( "another table for 4 small dishes and 3 larges dishes was $23.30. How much is each a small and
\n" ); document.write( "large dish alone? \n" ); document.write( "
Algebra.Com's Answer #847526 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "x = cost of 1 small dish
\n" ); document.write( "y = cost of 1 large dish
\n" ); document.write( "Each cost is in dollars.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3 small + 5 large = $28.20
\n" ); document.write( "3x+5y = 28.20\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "4 small + 3 large = $23.30
\n" ); document.write( "4x+3y = 23.30\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "We can form this system of equations
\n" ); document.write( "\"system%283x%2B5y+=+28.20%2C4x%2B3y+=+23.30%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's say we want to eliminate the x variable.
\n" ); document.write( "If we add the equations straight down we get 3x+4x = 7x, but we want the x values to go to 0.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "We can quadruple both sides of the original equation.
\n" ); document.write( "Also we can multiply both sides of the 2nd equation by -3 to get this equivalent system.
\n" ); document.write( "\"system%2812x%2B20y+=+112.80%2C-12x-9y+=+-69.90%29\"
\n" ); document.write( "At this point the x coefficients are equal in absolute value, but have opposite sign.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Add straight down.
\n" ); document.write( "The x terms add to 0.
\n" ); document.write( "The y terms add to 11y
\n" ); document.write( "The right hand sides add to 42.90\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "We arrive at 11y = 42.90
\n" ); document.write( "Divide both sides by 11 to get y = 42.90/11 = 3.90
\n" ); document.write( "This result is exact and hasn't been rounded.
\n" ); document.write( "One large dish costs $3.90\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since we know the value of y, we can use it to find x.
\n" ); document.write( "Use any of the equations mentioned.
\n" ); document.write( "3x+5y = 28.20
\n" ); document.write( "3x+5*3.90 = 28.20
\n" ); document.write( "3x+19.50 = 28.20
\n" ); document.write( "3x = 28.20-19.50
\n" ); document.write( "3x = 8.70
\n" ); document.write( "x = 8.70/3
\n" ); document.write( "x = 2.90
\n" ); document.write( "This result is exact and hasn't been rounded.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------------------------------------------------------------------
\n" ); document.write( "--------------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answers:
\n" ); document.write( "One small dish costs $2.90
\n" ); document.write( "One large dish costs $3.90
\n" ); document.write( "I'll leave the verification for the student to do.
\n" ); document.write( " \n" ); document.write( "
\n" );